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COPYRIGHT DEPOSIT. 





































































































































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*; 








Celo-Navigation 


Commander Benjamin Dutton, U.S.N. 


1924 










\ 


Copyright, 1924, by 
U. S. NAVAL INSTITUTE 
Annapolis, Maryland 



THE INDUSTRIAL PRINTING COMPANY 
BALTIMORE, MARYLAND 


DEC I,S -1924 

'' ©Cl A 81 5215 




CONTENTS 


PAGE 

Chapter I. Time. 3 

Chapter II. Observations for Latitude. 19 

Chapter III. Azimuth. 33 

Chapter IV. Lines of Position. 40 

Chapter V. A Navigator’s Work at Sea. 54 












CELO-NAVIGATION 


PREPARED FOR USE AT THE U. S. NAVAL ACADEMY 


By 


Commander Benjamin Dutton, U. S. Navy 






FOREWORD. 


Beginning with the issue for 1925, the data of the Nautical Almanac is to be 
tabulated for civil time instead of astronomical time. The change in the Nautical 
Almanac having made necessary a new text on Celo-Navigation, this pamphlet has 
been prepared by Commander Benjamin Dutton, U. S. Navy. Various officers of the 
Department of Navigation have assisted by criticizing the text and by preparing and 
checking the problems. The text is not complete, as it is intended to replace only 
those parts of Navigation, 1922, which have been rendered obsolete by the change 
in the Nautical Almanac. 


22 August, 1924. 


CHAPTER I. 

TIME. 


1. Time, for general use, is measured by the apparent movement of an imaginary 
body called the mean sun. This is called mean time, and is used as a measure of dura¬ 
tion. The navigator has an additional use for time, that of determining the position 
of the celestial bodies relative to his meridian. For this purpose he requires two other 
kinds of time. For determining the position of the true sun he requires a time based 
upon the apparent movement of that body. This is apparent time. For other celestial 
bodies he requires a time measured by the apparent movement of the stars. This is 
sidereal time. 

The apparent movements of the celestial bodies are caused by the real movement 
of the earth. It is the purpose of the following discussion to show how the movement 
of the earth causes the mean sun, the true sun, and the stars to appear to move at 
different rates and to make clear the uses and the relations of the different kinds of 
time based upon those different rates of movement. 

The earth has two distinct motions: 

First, a perfectly uniform rotation to the eastward about its axis. There are 
366.24+ rotations in the period of time called a solar year. Each of these rotations 
takes place in exactly the same period of time and at a uniform rate. 

Second, one yearly revolution to the eastward about the sun, in the plane of the 
ecliptic. Each of these revolutions is completed in the same period of time, but since 
the orbit of the earth about the sun is an ellipse, and since the earth moves at a 
varying speed in that orbit, the angular rate of the movement is constantly varying 
throughout the year. 

The effect of these two motions of the earth in causing the apparent motion of 
'the sun is as follows: Although both the motions of rotation and revolution are in 
the same direction, to the eastward, the apparent revolutions of the sun which they 
cause, are in opposite directions. Thus, the rotation to the eastward will cause any 
celestial body to appear to revolve to the westward, while the revolution will cause 
the sun, which is within the orbit, to appear to revolve to the eastward. See Figure 1. 


Figure 1. 


Effect of Rotation. 



The sun will successively transit meridians 1, 2, and 3, 
or apparently move to westward. 


Effect of Revolution. 



3 





4 


TIME. 


The sun’s apparent yearly motion therefore has two components, which are, first, 
366.24+ revolutions to the westward at a uniform rate, caused by the earth’s rota¬ 
tion, and second, one yearly revolution to the eastward at a varying rate, caused by 
the earth’s revolution. The net result is that the sun makes 365.24+ yearly revolu¬ 
tions to the westward, at a varying rate. 

Due to the inclination of the planes of the ecliptic and the equinoctial, the sun’s 
variable motion in the ecliptic becomes more variable when projected on the equinoc¬ 
tial, where hour angles are measured. It is evident that the rate of change of the 
sun’s hour angle is not uniform. 

As the sun’s apparent motion causes our periods of darkness and light, as well as 
the cycles of the seasons, it is the natural measure of time. Since, however, as explained 
above, its rate of change of hour angle is not uniform, it does not provide a practical 
measure because the units of time as determined by its motion are of constantly vary¬ 
ing lengths. To obviate this disadvantage, and to retain the advantage of a time 
measurement based upon the motion of the sun, an imaginary sun called the mean 
sun is used. 

2. The Mean Sun. This is an imaginary sun which moves to the eastward in 
the equinoctial at a uniform rate equal to the average rate of the true sun in the 
ecliptic. (See Figure 1.) Due to the earth’s revolution about the sun, the latter 
appears to move in the ecliptic at an average daily rate of 3 m -56 8 .6. Therefore the 
mean sun is supposed to move uniformly at that rate in the equinoctial, t. e., to increase 
its right ascension 3 m -56 8 .6 every day. Under this assumption both components 
of the apparent motion of the mean sun are uniform. Its total motion is therefore 
uniform, and the units of time as measured by its movement are of unvarying length. 

3. Mean Time. Time as measured by the apparent motion of the mean sun 
is called mean time. In mean time the mean solar day is the interval of time required 
for the mean sun to make one apparent revolution about the earth. Formerly navi¬ 
gators considered the day as beginning at the instant the sun crossed the upper branch 
of the meridian, i. e., at noon. Mean time, with the beginning of the day, at that 
instant, is called astronomical time. Navigators now use the instant of transit of the 
sun across the lower branch of the meridian (midnight) as the beginning of the day. 
Time so reckoned, i. e., by the apparent motion of the mean sun with the instant of 
lower transit as the origin of the day, is called civil mean time, or more commonly, 
civil time. In general practice the twenty-four hours which constitute the day are 
divided into two equal periods of twelve hours each. The period next succeeding the 
lower transit is indicated by writing A.M. after the hours, and the period next suc¬ 
ceeding upper transit indicated by writing P.M. after the hours. For navigational 
purposes the hours are numbered from zero at lower transit to twenty-four hours at 
the next lower transit, and the suffixes a.m. and p.m. are omitted. 

From this point on, the term civil time will refer to civil time with the hours 
numbered from 0 to 24, and times given as civil times will be so numbered. 


CIVIL TIME AND THE HOUR ANGLE OF THE MEAN SUN. 

4*.. day begins at the instant of the lower transit of the mean sun 

the civil time at any place at any instant is equal to the hour angle of the mean sun 
as measured from the lower branch of the meridian at that instant. 

Later on, in dealing with sidereal time, it will be found convenient to restate the 
above as follows: Hour angles are measured from the upper branch of the meridian 
therefore, at the beginning of the civil day, at lower transit, the hour angle of the 
mean sun is twelve hours. From this instant, as the sun advances to the westward 
the hour angle of the sun and the civil time increase in unison, so that the civil time 
is always equal to the hour angle of the mean sun plus twelve hours, dropping twentv- 
four hours if the sum exceeds that amount. 


TIME. 


5 


Tn, 


Let S be the mean sun. 


S 



Let PG, be the meridian of Greenwich, 
and PMi and PM 2 the meridians of two 
other places, Pmi and Pm 2 being the 
lower branches. Then GMi and GM 2 
are the longitudes of PMi and PM 2 . 
Gall these XI and \2. 


MiS and M 2 S are the hour angles of the 
sun from Mi and M 2 . Call these ti and t 2 . 


Then Ti and T 2 (see figure), will be 
the civil times for the meridians PMi 
and PM 2 . By inspection 


(1) Hence the local civil times at any 
two places differ as the hour angles of 
the mean sun as measured from those 
places. 


Ti = ti + 12 
and T 2 =t 2 + 12. 


Fig. 2. 


Now, by inspection, \ 2 — \i = Mi M 2 



(2) Or the hour angles of the sun from two places differ as the longitudes of 
those places. 

Pmi and Pm 2 being the lower branches of the meridians of PMi and PM 2 , the 
times at Mi and M 2 are Ti and T 2 
Ti — T 2 = mi m 2 = Mi M[ 2 = X 2 Xi 

(3) .*. At any two places the local civil times differ as the longitudes of those 


places. 


(4) Hour angles are measured to the westward, therefore of two meridians, that 
one which is farthest to the east will have the largest hour angle and the later time. 

(5) Combining (3) and (4)—'The local times at any two places differ as the longi¬ 
tudes of those places, and the place farthest east has the later time. 


CONVERSION OF ARC AND TIME UNITS. 


5. As longitudes are expressed in units of arc, and hour angles and time are 
expressed into time units, it becomes necessary to convert arc units into time units 
before applying the above rules. The relationship between the two sets of units is 
based upon the fact that the sun completes its apparent revolution of 360° of longitude 
in 24 hours, and therefore 1 hour of time = 15° of arc. Also, 1 minute of time = 15' 
of arc, and 1 second of time = 15" of arc. Therefore a given number of degrees, 
minutes, or seconds of arc may be converted to hours, minutes, or seconds of time by 
dividing by 15. 

Since 15° of arc equal 1 hour, or sixty minutes of time, 1° of arc equals 4 minutes 
of time. Therefore if a given number of degrees of arc is not exactly divisible by 15 
the conversion to time may be completed by simply multiplying the remainder by 
four and denoting the product as minutes of time, thus:— 

Reduce 43° to time units. 


_ = 2 with remainder 13 = 2 hours and 52 minutes. 


The same reasoning will hold for reducing minutes of arc to minutes of time. 




6 


TIME. 


Thus, reduce 43' to time. 


= 2 and 13 over 
15 


2 minutes and 52 seconds. 


Now reduce 43°-43' to time units. 

43° 

— =2 with remainder 13 = 2 hours 52 minutes. 


43' 

15 


= 2 with remainder 13 = 


2 minutes 52 seconds. 


43°—43' =2 hours 54 minutes 52 seconds. 

A remainder left over when dividing seconds of arc by 15 must be carried as a 
fraction of a second of time or preferably reduced to a decimal. (The nearest tenth 
is sufficiently accurate in navigation.) 

In practice the form for work is more convenient as shown below: 

Reduce 43°-43'-43" to time units. 

15/43°-43' -43" 

2 -52 
2 -52 
2tt 

2 h -54 m -54 s .9 

Problems. Convert into time: Answers: 

29°-43'-30". ih_58 m 54 8- 

155°-13'-43". i()ii-20m-54.87-. 

177°-15'-30". ll h -49 m -02 s . 

CONVERTING TIME INTO ARC. 

Since 1 hour of time = 15° of arc, a given number of hours may be converted 
to degrees of arc by simply multiplying by 15. Similarly a given number of minutes 
of time may be converted into minutes of arc by multiplying by 15, but, as the product 
will usually exceed 60', it must be further reduced to degrees and minutes by dividing 
by 60. Thus: 10 minutes of time = 10X15 minutes arc = 150' = 2°-30'. The same 
result is obtained more directly by remembering that any number, as x, of minutes 

of time is equal to — hours of time. Converting hours of time to degrees of arc as 

before by multiplying by 15, we have ^ X15 = ^ = ~ degrees. Thus 23 minutes of 
23 

time = — degrees of arc, = 5°-45'. 

Convert 2 h -30 m -27 8 of time to arc. 

2 h = 30° 


Qn° 

30 m = ^-= 7°-30' 

4 

27' 

27 s =^j- = 6'-45" 

37°-36'-45" 

Or the work may be done more conveniently in the following form: 

2 h -30 m -27 8 

30° 

7°-30' 

6'-45" 


37°-36'-45" 








TIME. 


7 


Problems. Convert into arc: Answers: 

6 h -15 m -32 8 93°-53'-00" 

10 h -53 m ^45 8 163°-26-15" 

Hh_3 5 m_i5s 173°-48'-45" 


RELATIONS OF LOCAL TIMES AND DATES AT TWO PLACES. 

6. Knowing the longitude of a place and the local time at that place, the time 
at another place of known longitude may be found from (5), by first converting the dif¬ 
ference in longitude between the two places to time units and applying it to the known 
time at the first place, adding if the second place is east of the first, and subtracting 
if it is west. 

Problem: At a place, A, whose longitude is 75° W., the time is 17 h . Find the time at the same 
instant at Greenwich, and at places whose longitudes are 150° W., and 30° E. Ans. 22 h , 12 h , 0 h . 

When the sum of the time at one place plus the difference in longitude between 
the two places is greater than twenty-four, twenty-four hours must be dropped from 
the time and one added to the date of the second place. 

Problem: Place A, longitude 47°-23' W., times 7 h -10 m , April 23rd; 22 h -13 m -27 s , April 23rd. 
Find the corresponding times in a place whose longitude is 47°-23' E. Ans. 13 h -29 m -04 s , April 23rd; 
4 h -32 m -31 s , April 24th. 

When the second place is west of the place whose time is known, and the dfference 
in longitude is greater than the known time, it is necessary to add 24 hours to the time 
and subtract one from the date before applying the difference in longitude. Thus, 
suppose at a place in 50°-27' west longitude, the time is l h -43 m , April 23rd, and it 
is desired to find the time at a place whose longitude is 158°-18' west. The difference 
in longitude is 107°-51' = 7 h -ll m -24 s . The time at the first place is l h -43 m , April 
23rd, or 25 h -43 m , April 22nd. Subtracting the longitude from the latter, the time at 
the second place is 18 h -31 m -36 s , April 22nd. 

Problems: The longitudes of certain places and the times at those places are given in the first 
and second columns below. Find the corresponding times and dates at places whose longitude appears 
in the third column. 


1 . 

120°-13'-00" W. 

10 h -51 m -00 s , Feb. 1 

90°-13' W. 

2. 

“ “ “ 

“ “ “ “ “ 

90°-13' E. 

3. 

“ “ “ 

“ “ “ “ “ 

44°-47' E. 

4. 

“ “ “ 

“ “ “ “ “ 

89°- 47' E. 

5. 

75°-13'-00" W. 

lh_03m-00 s , Sept. 21 

30°-00' W. 

6. 

“ “ “ 

105°-00' W. 

7. 

60°-13'-00" E. 

16 h -16 m -32 s . Dec. 31.1924 178°-13' E. 

8. 


“ “ “ “ 

“ 160°-00' E. 

5WERS : 



1 . 

12-51-00, Feb. 1. 

5. 

4-03-52, Sept. 21. 

2. 

0-52-44, Feb. 2. 

6. 

23-03-52, Sept. 20. 

3. 

21-51-00, Feb. 1. 

7. 

0-08-32, Jan. 1, 1925. 

4. 

0-51-00, Feb. 2. 

8. 

22-55-40, Dec. 31, 1924. 


GREENWICH CIVIL TIME AND DATE. 

7. When a navigator takes an observation of a heavenly body for the purpose 
of determining his position at sea, he obtains only one of the coordinates of that body 
by observation. This is the altitude. Before he can solve the astronomical triangle 
to determine his position, he requires certain other data, such as the body’s declina¬ 
tion, or the right ascension of the mean sun. The Nautical Almanac tabulates these 
data in such a way that they may be found for any instant of Greenwich civil time. 
To use this tabulated data the navigator must determine the Greenwich civil time 
and date corresponding to the instant of his observation. This he does by noting 
the time of observation by the chronometer which is regulated to keep Greenwich 
civil time. However, since the chronometer face is graduated from zero to twelve 
hours, instead of zero to twenty-four, the Greenwich civil time, in which the hours 
are numbered from 0 to 24, may vary from the chronometer reading by twelve hours. 


8 


TIME. 


Of course, the chronometer does not indicate the Greenwich date, which may be 
different from the navigator’s local date by one day. All the chronometer gives the 
navigator is the Greenwich civil time with a liability of error of exactly 12 hours. 
But the navigator knows the local date, approximate local civil time, and approxi¬ 
mate longitude. With these he determines the Greenwich date and approximate 
time, and from the latter determines whether it is necessary to add twelve hours to 
the reading of the chronometer to get the exact Greenwich civil time of the instant 
of his observation. 

Examples: At about 4:00 p.m., 2 February, a ship’s D.R. longitude is 72°-32' W. The navigator 
r sun i usm £ a wa tch set to local civil time, and obtains the following time data: W 4-03-27, 

C.-W 4-57-55, chro. fast 2 m -01 s . Find the Greenwich date and civil time. First find the Greenwich 
date and approximate time, thus: 


Local civil time 

16-03-27, 2 Feb. 


Long. 

4-50-08 (west) 


Gr. approx, civil time 20-53-35, 2 Feb. 

Hence 12 hours must be added to the chronometer 
reading. 

Now find the exact Greenwich time, thus: 


W. 

4-03-27 


C-W 

4-57-55 


Chro. face 

9-01-22 


Chro. fast 

2-01 


Chro. 

8-59-21 (add 12) 


Gr. civil time 

20-59-21, 2 Feb. 



Or the same results may be obtained by means of a time diagram (Figure 3) 
which is constructed as follows for the data above: 


w Draw a circle to represent the equinoctial. 

P, its center, is the pole. Its circumference is 
considered to be divided into 360° or 24 h , as the 
case may require. Draw mPM vertically to 
represent the local meridian, dotting mP, the 
lower branch. Draw a small circle on the equi¬ 
noctial to represent the sun. Place this circle at 
an angular distance from the lower branch of 
the meridian equal to the local civil time, repre¬ 
senting the westward direction as clockwise. 
Draw the sun’s hour circle, OP. Now draw the 
Greenwich meridian, GPg, so that the local 
meridian will be to the east or west of it, ac¬ 
cording as the longitude is east or west, and at 
a distance equal to the local longitude. Draw 
the dotted arrow to indicate the hour circle of 
the sun from the lower branch of the Greenwich 
, _ . meridian. This is the Greenwich civil time. It 

then will be apparent whether the Greenwich civil time is greater or less than twelve 
hours. I he Greenwich date and the local date will be the same unless the sun is in 
the smaller sector between the lower meridians. In the latter case, if the sun is 
to the west of the Greenwich lower meridian, the Greenwich date is one more than 
the local date, and if to the east, one less. Exactness is not required in these diagrams 
They may be drawn free hand. 8 



Fig. 3. 






TIME. 


9 


Examples: 


Local civil time 
Longitude 

8 h 

60° 

1 April. 
East. 

> Upper Figure. 

Greenwich civil time 
Ijocal civil time 
Longitude 

4 h 

19 h 

60° 

1 April. 

1 April. 
East. 

J 

j Second Figure. 

Greenwich civil time 

15 h 

1 April. 
21 Sept. 
West. 

Local civil time 
Longitude 

16 h 

150° 

1 Third Figure. 

Greenwich civil time 
Local civil time 
Longitude 

2 h 

8 h 

150° 

22 Sept. 
21 Sept. 
East. 

J 

j> Lower Figure. 

Greenwich civil time 

22 h 

20 Sept. 


Problems: Given the following data, find the Greenwich civil time 
and date. 


Watch Time. 

C-W. 

Chro. Error. 

Approximate 

Longitude. Date. 

1 . 

6-30-50 

7-45-10 

2 m -20 s slow 

100 ° w. 

Jan. 2, a.m. 

2. 

10-50-51 

7-12-25 

l m -27 s fast 

72° E. 

May 4, a.m. 

3. 

4-02-19 

4-03-49 

3 m —01 s slow 

61° W. 

Jan. 19, p.m. 

4. 

5-59-00 

8-42-25 

0 m -26 8 fast 

49° E. 

May 3, p.m. 

5. 

6-05-30 

9-02-48 

l m -42 s slow 

136° W. 

Jan. 10, p.m. 

6. 

5-50-10 

1-27-04 

l™—01 s fast 

159° E. 

Jan. 24, a.m. 

7. 

3-20-00 

10-03-24 

2“-02 8 fast 

150° W. 

May 29, p.m. 

8. 

11-15-00 

1-43-01 

1™—59 s slow 

26° W. 

Jan. 14, p.m. 

9. 

6-02-56 

3-00-06 

2 m -00 8 slow 

135° E. 

May 19, a.m. 

Answers : 






1. 14-18-20, Jan 2. 4. 14-40-59, May 3. 7. 1-21-22, May 30. 

2. 6-01-49, May 4. 5. 3-10-00, Jan. 11. 8. 1-00-00, Jan. 15. 

3. 20-09-09, Jan. 19. 6. 19-16-13, Jan. 23. 9. 21-05-02, May 18. 

GAIN OR LOSS OF TIME WITH CHANGE OF POSITION. 

8. It has been shown that local noon at any meridian is 
the instant when the sun is on the upper branch of that 
meridian, that at all places east of that meridian at that in¬ 
stant it is past noon, or time is fast of that of the given 
meridian; at all places west of that meridian it is not yet 
noon, or time is slow of that of the given meridian. Hence 
it is evident that if a navigator travels east, carrying a watch 
regulated to the time of the meridian departed from, and if 
he desires to set the watch to the time of a meridian to the 
eastward, he must set it ahead at the rate of 1 hour for every 
15° change of longitude, or 24 hours for every 360°. 





GREENWICH NOON. 

9. The instant of Greenwich noon is one of 
particular interest to navigators, for it is at this 
instant, and at this instant only, that the same 
date prevails throughout the earth. This is 
shown in Figure (a), in which PG is the meridian 
of Greenwich, and Pg is the 180th meridian. 
Assume a date for the figure, say May 2nd. Then 
the time and date at Greenwich being 12 hours 
of May 2nd, the date over the entire world is 
May 2nd, and the time on every 15th meridian 
will be as shown. Note, however, that on the 
180th meridian the time of this instant may be 
expressed as either 0 hours or 24 hours of May 
2nd, according as the longitude is reckoned as 
west or east. Now 24 hours of May 2nd may be 
expressed as 0 hours of May 3rd. This is the 
first instant that the date May 3rd has been in 
effect anywhere on the earth. Therefore, mak¬ 
ing a general case, a new date first comes into 
effect on the earth at the 180th meridian at the instant of Greenwich noon. 



(a) 







10 


TIME. 


CROSSING THE 180TH MERIDIAN. 

10. The figures that follow are intended to illustrate the advance over the world 
of the new date which came into effect as explained above. They cover the period 
of 24 hours next succeeding a Greenwich noon. As before, PG and Pg are the meridians 
of Greenwich and 180°, O is the sun, PO the meridian the sun transits at the various 
instants for which the figures are drawn, and Ps is the lower branch of that meridian. 
The area in which the date of May 2nd is in effect is shaded, and the unshaded area 
is that in which the date of May 3rd is in effect. 






U) 


Figure (b) shows the situation a short time after 
the instant of 0 hours of May 3rd at the 180th me¬ 
ridian. The sun has crossed the lower branches 
of all meridians in the sector gPs, and therefore 
the date of May 3rd is in effect in that sector. 

As the sun continues to move to the west, as 
shown in Figures (c), (d), and (e), it will be seen 
that the sector gPs constantly increases in size due 
to the movement of the line Ps, which moves with, 
but 180° behind, the sun. From an examination 
of the figures it is apparent that, except at the in¬ 
stant of Greenwich noon, there are always two 
dates in effect, and that the larger date covers a 
sector which begins at the 180th meridian and in¬ 
creases to the westward with the movement of the 
sun. Therefore, if you cross the 180th meridian 
when traveling westward, you arrive in the sector 
where the date is one larger than in the sector you 
just left, and if traveling eastward, you arrive in 
(sc J the sector where the date is one less. Hence the 
V. rule: When crossing the 180th meridian sailing 

westward add one to the date, and if sailing east¬ 
ward, subtract one from the date, at the same time 
changing the name of the longitude. The above 
rule applies to the date used by the navigator. To 
avoid the inconvenience of changing the name of a 
day while that day is in effect, the case is handled 
for ship’s time by dropping one day at midnight 
when the crossing is made westward bound, and 
repeating one day when eastward bound. 

A little consideration will show that, while the 
/ / x date j s changed upon crossing the 180th meridian, 

( J the .time is not changed. The latter is the hour 

V angle of the sun from the lower branch of the 

meridian and in the infinitesimally small period of 
time required to cross that imaginary line, the 
180th meridian, there is no change in the sun’s 
hour angle. 


APPARENT TIME. 

11. Time as measured by the apparent motion 
of the true sun is called apparent time. An apparent 
solar day at any place is the interval of time between 
\ two successive transits of the true sun across the 
/ )°wer branch of its meridian, and the time of day 
i® the hour angle of the sun plus twelve hours, drop- 
ping twenty-four hours if the sum exceeds twenty- 
four hours. Apparent noon at a place is the instant 
of the true sun s transit of the upper branch of the 
meridian of that place, when its hour angle is zero. 






































TIME. 


11 


Apparent time at any instant differs in amount from the mean time of the instant 
by the difference in the hour angles of the mean and apparent suns, or, what is the 
same thing, by the difference in their right ascensions. This difference is called the 
equation of time. It has a maximum value of about sixteen minutes and reduces to 
zero four times during a year. During two periods of the year the mean sun is ahead 
of the true sun, so that the mean time is greater than the apparent time, and during 
two periods the reverse is true. 

The equation of time is tabulated in the Nautical Almanac (pages 6-29) for every 
even hour of Greenwich civil time for every day of the year, and may be found for 
any intermediate instant by interpolation. For convenience in interpolating, the 
hourly difference in the equation is given for each day. The Nautical Almanac also 
gives the sign (+ or —) to be used in applying the equation of time to mean time. 

TO FIND THE L.A.T. AT A PLAGE AT ANY INSTANT. 

Find the G.G.T. and date of the instant, and for this G.C.T. and date select the 
equation of time from the Nautical Almanac. Apply this equation of time to the 
G.G.T. in accordance with the sign as given. The result will be G.A.T. Apply the 
longitude of the place to the G.A.T. The result will be L.A.T. 

TO CONVERT APPARENT TO MEAN TIME. 

12. The equation of time is not tabulated in the Nautical Almanac for apparent 
time, so that exact conversion of apparent to mean time is not readily accomplished. 
However, the results will be close enough for most purposes if the equation is selected 
from the Nautical Almanac with the apparent time as though the latter were mean 
time, and applied to the apparent time with the sign reversed. If a closer approximation 
is desirable, the equation of time may be selected for the mean time instant as found 
above, and this second equation of time applied to the apparent time. 

If the apparent sun is substituted for the mean sun in Figure 2, it readily can be 
shown that the hour angles of the apparent sun, and the local apparent times, at any 
two places differ as the longitudes of those places. 

USES OF APPARENT TIME. 

13. When the navigator observes the sun to determine his position, or to deter¬ 
mine the error of the compass, one of the coordinates he requires is the sun’s hour 
angle, which is found by the use of local apparent time. 

FINDING THE HOUR ANGLE OF THE SUN. 

14. The local apparent time is equal to the hour angle of the sun plus twelve 
hours, dropping twenty-four hours if the sum exceeds that amount. In finding the 
hour angle of the sun from the local apparent time it is convenient to state this in 

(a) (b) 




a different way. Refer to the figures below. In Figure (a), let the sun be any¬ 
where west of the meridian. It will be seen that L.A.T. = H.A. + 12 hours. In 
Figure (b), let the sun be anywhere east of the meridian. It will be seen that in 
this case L.A.T. = H.A. —12. 





12 


TIME. 


Two cases for finding the sun’s hour angle result from the above: 

(1) Sun west of the meridian, L.A.T. = H.A. + 12 h , and H.A. = L.A.T. —12 h . 

(2) Sun east of the meridian, L.A.T. = H.A. —12 h , and H.A. = L.A.T.+ 12 h . 

Problems: 

Given the following data, find the Greenwich apparent time and thence the local apparent time 
and the H.A. of the sun at the place whose longitude is given. 



Watch. 

C-W. 

Chro. Error. 

Long. 


Date. 

1 . 

8-04-31 

4-14-08 

l m -49 s fast 

68°-17'-00" 

w. 

May 1, p.m. 

2. 

4-05-22 

5-14-28 

l m -49 s fast 

68°-17'-00" 

w. 

May 1, p.m. 

3. 

4-51-20 

3-31-23.5 

3 m -41.1 8 slow 

121°-08'-25" 

E. 

Jan. 3, a. m. 

4. 

4-22-16 

3-51-20.5 

3“—41.1 s slow 

121°-08'-25" 

E. 

Jan. 3, p.m. 

5. 

11-01-01 

1-57-54 

l m -05 8 slow 

30°-00'-00" 

W. 

Jan. 2, p.m. 

6. 

1-01-07 

9-57-48 

l m —05 s slow 

30°-00'-00" 

E. 

Jan. 2, a.m. 

7. 7-07-19 

Answers: 

2-44-42 

4 m -01 8 fast 

i39°-30'-oo" 

E. 

Jan. 4, a.m. 


1. G.A.T. 00-19-48.9, L.A.T. 19-46-40.9; H.A. 7-46-40.9. 

2. G.A.T. 21-20-59, L.A.T. 16-47-51.0; H.A. 4-47-51.0. 

3. G.A.T. 20-22-11.3, L.A.T. 4^26-17.2; H.A. 16-26-45.0. 

4. G.A.T. 8-12-50.5, L.A.T. 16-17-24.2; H.A. 4-17-24.2. 

5. G.A.T. 0-55-41.4, L.A.T. 22-55-41.4; H.A. 10-55-41.4. 

6. G.A.T. 22-56-11.8, L.A.T. 0-56-11.8; H.A. 12-56-11.8. 

7. G.A.T. 21-42-50, L.A.T. 19-00-50; H.A. 5-59-10.0. 

8. Find to the nearest tenth of a second the L.C.T. of a place whose longitude is 75° W., at the 
instant the L.A.T. is 8-00-00, October 4, 1925. 

Answer: 7-48-49. 


FINDING THE TIME OF TRANSIT OF THE SUN. 


15. The instant of the transit of a celestial body is of particular use to the 
navigator because at this instant the latitude is most readily and accurately deter¬ 
mined. For the sun the instant of transit is local apparent noon, and when the longi¬ 
tude is known, is predicted as follows: 

At the instant of local apparent noon the L.A.T. is 12 h -00 m -00 s . The longitude 
applied to this time, will give the G.A.T. of local apparent noon. For this instant 
the equation of time is selected and applied to the G.A.T., with sign reversed, the 
result being the G.G.T. of L.A.N. To this the chronometer error is applied, and the 
result is the chronometer reading at local apparent noon. The navigator’s watch is 
then compared with the chronometer, and C-W obtained. This, subtracted from the 
computed chronometer time of L.A.N. will give the watch time of local apparent noon. 


Example: Find the watch time of local apparent noon on October 4, 1925, at a place whose longi¬ 
tude is 63°-53' W. The chronometer is fast 01 m -27 8 , C-W 4 h -04 m -16 8 . 


L.A.T. of L.A.N., 
Long. W., 

G.A.T. of L.A.N., 

Eq. T. (sign reversed), 

G.C.T. of L.A.N., 
Chron. error, fast, 

Chro. face at L.A.N., 
C-W, 

Watch time of L.A.N., 


12-00-00 Oct. 4. 
4-15-32 


16-15-32 Oct. 4. 
(-) 11-13.4 

16-04-18.6 

1-27.0 


16-05-45.6 
(-) 4-04-16 


12-01-29.6 


Problems: Find the watch time of L.A.N. in the following cases. 


Longitude. 


Date. 

Chro. Error. 

C-W. 

1. 23°-17' E. 


May 2 

2“-21.1 s slow 

10-23-00 

2. 58°-26'-30" 

W. 

Jan. 1 

l“-05 8 fast 

3-04-51 

3. 177°-45' E. 


Oct. 4 

l m -59.2 8 slow 

11-58-46 

4. 120°-16'-15" 

W. 

July 1 

1 "*-31.1 s fast 

8-02-10 

Answers : 

1. 11-58-29. 

2. 

12-53-39.8. 

3. 11-57-13.8. 

4. 12-04-03. 






TIME. 


13 


SIDEREAL TIME. 

16. In the presentation of the subject of solar time it was shown that while 
the earth rotates upon its axis 366.24 + times a year, the sun makes only 365.24 + 
apparent revolutions, the loss of one apparent revolution being caused by the earth’s 
revolution about the sun. In the case of the stars the earth’s revolution does not 
have the same effect, for the stars are at such a great distance outside of the earth’s 
orbit that the latter is of insignificant size and the earth’s movement in it causes no 
apparent motion of the stars. This being so, the apparent motion of the stars is 
caused solely by the earth’s rotation. It is therefore uniform and at the rate of 366.24 + 
revolutions per year. The rate of change of hour angle of the stars is therefore different 
fiom the rates of both the true and the mean suns, so that neither apparent nor mean 
time can be used directly to determine star’s hour angles. For this purpose it is 
necessary to use a time based upon the apparent motion of the stars. This is known 
as sidereal time. 

The vernal equinox being at an infinite distance from the earth, its apparent 
motion, like that of the stars, is unaffected by the earth’s revolution. Its rate of 
change of hour angle therefore serves as a measure of sidereal time. Since the vernal 
equinox also serves as the point of origin for the measurement of right ascensions, 
which are similar to hour angles, but measured to the eastward, there is a definite 
relationship between sidereal time and right ascensions. 

The sidereal day is the interval of time between two successive upper transits 
of the vernal equinox at the same meridian. It is divided into twenty-four hours 
numbered from 0 to 24. 

The sidereal time at any place at any instant is equal to the hour angle of the 
vernal equinox from that place at that instant. Note the difference from solar time 
which is equal to the hour angle of the sun plus twelve hours, the difference being due 
to the fact that the sidereal day begins at upper transit of the vernal equinox and 
the solar day at lower transit of the sun. Sidereal noon at a place is the instant of 
the upper transit of the vernal equinox at that place. 

If the vernal equinox is substituted for the mean sun in Figure 2, it may be shown 
that the sidereal times at two places differs as the longitudes of those places. 

RELATION BETWEEN CIVIL AND SIDEREAL TIME. 

17. An expression which represents the civil time of an instant may be inter¬ 
preted in two ways. First, it may be read as an expression of the angular distance 
of the mean sun from the lower branch of the meridian. Second, it may be used as 
an expression of the amount of duration that has elapsed since the mean sun crossed 
the lower branch of the meridian. Similarly an expression which represents the 
sidereal time of an instant may be used in the same two ways, first as an expression 
of the angular distance of the vernal equinox from the meridian, and secoftd, as an 
expression of the amount of duration that has elapsed since the vernal equinox crossed 
the meridian. It is evident that when a civil time and a sidereal time are used in 
the first sense, as expressions of angular measurement, they are in the same units, 
those of angular measurement. In this sense a civil time and a sidereal time may be 
combined without conversion, just as any angular measurement may be added to or 
subtracted from another angular measurement to obtain their sum or difference. 

When a sidereal time and a civil time are used as expressions of duration, as 
distinguished from expressions of position, they are in different units. Since a solar 
year is equal to 365.2422 civil days or 366.2422 sidereal days, the relation between 
the two sets of units is obtained from the fact that 365.2422 civil days equal 366.2422 
sidereal days. The sidereal day is shorter than the civil day by 3 minutes, 55.909 
seconds of mean solar time; and sidereal hours, minutes, and seconds are proportion¬ 
ally shorter than civil hours, minutes, and seconds. 

Since the units of civil and sidereal time represent unequal amounts of duration, 
two periods of time, one expressed in civil units, and the other sidereal units, cannot 
be combined to find the sum oi difference of the periods without converting one to 
the terms of the other. This may be accomplished readily by means of Tables II 
and III of the Nautical Almanac, or Tables 8 and 9 of Bowditch, the computation 
of these tables being based on the relationship explained in the preceding paragraph. 


14 


TIME. 


RELATION OF THE SIDEREAL TIME TO THE HOUR ANGLE AND RIGHT ASCENSION 

OF ANY BODY. 

18. In the diagrams of Figure 5, the circle represents the equinoctial, and P 
the pole. PM is the meridian of any place, PB the hour circle of a celestial body, 
and T is the vernal equinox. The arc M T representing the local sidereal time (L.S.T.) 
of the place is shaded. The right ascension (RA) and the hour angle (HA) of the 
body are indicated by dotted lines. 


Figure 5. 

Case I Case II Case III 





In Case I, the hour circle of the body is within the arc which measures the local 
sidereal time. By inspection L.S.T. = RA + HA. 

In Case I, the hour angle plus the right ascension cannot exceed 24 hours. There 
are two other possible cases, and in these the sum of the hour angle plus right ascen¬ 
sion must exceed 24 hours. 

In Case II, the hour circle of the body is outside the arc which measures the local 
sidereal time, and to the west of the local meridian. 

L.S.T. = MPB - T PB = H A - (24 - RA) = H A + RA - 24. 

In Case III, the hour circle of the body is outside of the arc which measures the 
local sidereal time but to the eastward of the local meridian. 

L.S.T. = BP T - BPM = RA - (24 - HA) = RA+HA - 24. 

Therefore, as these are the only possible cases, the local sidereal time of a meridian 
is equal to the right ascension plus the hour angle of a celestial body, dropping 24 
hours if the sum exceeds that amount. 

The above rule enables a navigator to determine sidereal time without the use 
of a sidereal clock. From his chronometer he obtains the Greenwich civil time. This 
is the hour angle of the mean sun from Greenwich plus 12 hours. The right ascension 
of the mean sun plus 12 hours may be found by the use of the Nautical Almanac 
for any instant of G.G.T. Since the same relation exists between the hour angle plus 
12 hours and the right ascension plus 12 hours, as exists between the hour angle and 
the right ascension, the G.C.T., as obtained by chronometer, and the R.A.M.S. + 12 
hours, as obtained from the Almanac, may be added to obtain the G.S.T. The local 
longitude applied to this will give the local sidereal time. 

In the above discussion the terms civil and sidereal time were both used in the 
first sense, as expressions of position, not as expressions of duration. The Greenwich 
civil time expressed the angular distance of the mean sun west of the lower branch 
of the meridian. To this was added the right ascension of the mean sun plus 12 hours. 
This, also, was an angular measurement. The sums of these two gave as a result 
another angle which expressed the distance of the vernal equinox west of the Greenwich 
meridian. This is all a matter of the position, relative to each other, of three points, 
the Greenwich meridian, the mean sun, and the vernal equinox. Now having by this 
means ascertained the hour angle of the vernal equinox, that is, the sidereal time, 
the latter term may be used in its second sense, as a measure of duration, and in this 
sense it means that at the instant under consideration, so many hours, minutes, and 
seconds, of sidereal time have elapsed since the vernal equinox crossed the meridian 
of Greenwich. 
















TIME. 


15 


TO FIND THE L.S.T. AT THE INSTANT OF AN OBSERVATION. 

19 . As proved above G.S.T. = G.C.T.+R.A.M.S. + 12 hours. Pages 2 and 3 of 
the Nautical Almanac tabulate the R.A.M.S.+ 12 hours for the instant of 0 hours 
at Greenwich for every day of the year. At the foot of these pages is a table headed: 
“Correction for Longitude from Greenwich.” This is the correction which must be 
applied to find the R.A.M.S.+ 12 hours for the instant of 0 hours at any other merid- 
ian, or to determine the change in the R.A.M.S. that has taken place in a given mean 
time interval after Greenwich 0 hours. It is in this second manner that the navigator 
most frequently uses the correction. In fact, for the beginner in navigation, it would 
be an aid to the understanding of sidereal time if the tables on pages 2 and 3 were 
headed “R.A.M.S.+ 12 hours at 0 hours, Greenwich Civil Time” and “Corrections 
for Greenwich Civil Time Past Greenwich 0 Hours,” since they are first used in those 
ways. 

The G.C.T. and date of the instant of any observation having been found by 
chronometer, the R.A.M.S.+ 12 hours is selected for 0 hours of the date, from page 
2 or 3 of the Almanac, and corrected for the time past Greenwich 0 hours by use of the 
table at the bottom of the pages. Or this correction may be made more conveniently 
without interpolation, by the use of Table III, pages 110-111 of the Almanac, or Table 
9 of Bowditch. The G.C.T. plus the corrected R.A.M.S.+ 12 hours will give the G.S.T. 
of the observation. The longitude is then applied to find the L.S.T. 

Although convenient, the use of Table III of the Almanac or Table 9 of Bowditch 
as described above, is sometimes misleading since those tables are named: “Mean 
Solar into Sidereal Time.” 

The use of these tables may be explained in this way. The number of sidereal 
units in a given period of duration is greater than the number of civil time units in the 
same period. This difference is caused by, and is equal to, the movement of the mean 
sun in right ascension during the period. Hence a tabulation of the larger number of 
sidereal units in a given civil time interval is also a tabulation of the increase in the 
sun’s right ascension in the interval, but when it is used as such the process is not one 
of conversion of time, but of determining the change in the sun’s right ascension. 

Example: Given the following data, find the L.S.T., Watch 6-40-20, C-W 4-26-19, Chro. slow 
2 m -05 s , Long. 67°-16' W., Date, 2 January, 1925, p.m. 


Watch 

6-40-20 


C-W 

4-26-19 


Chro. 

11-06-39 


Chro. slow 

2-05 


G.C.T. 

23-08-44 

2 Jan. 

R.A.M.S.+ 12 

6-44-27 


Cor. for G.C.T. 

3-48.1 


G.S.T. 

5-56-59.1 

(rejecting 24 hours) 

Long. W. 

4-29-04 

L.S.T. 

1-27-55.1 



FINDING THE HOUR ANGLE OF CELESTIAL BODIES. 

20 . The right ascension of any celestial body used in navigation may be found 
in the Nautical Almanac as will be explained later. Having found the local sidereal 
time in the manner described in the preceding paragraph, and the right ascension from 
the Nautical Almanac, the hour angle is found from the equation L.S.T. = HA+RA, 
or HA = L.S.T.—RA. 

For a Star. The right ascension of the principal navigational stars may be 
found for the first day of any month on page 94 of the Nautical Almanac. It will be 
noticed that the monthly change is very small, so that in the case of a star it will be 
sufficiently accurate to use the right ascension for the nearest first of the month. Pages 
98 and 99 give the right ascensions of certain additional stars for the first day of the 
year, together with a table of the annual variations with which a rough correction may 
be made for the month. 






16 


TIME. 


Example: Find the hour angle of the star a Lyrae (Vega) on 13 January, at the instant when 
the L.S.T. is 12-54-16. 

L.S.T. 12-54-16 

☆’s R.A. 18-34-21.8 (from p. 94, N.A.) 

H.A. 18-19-54.2 

For a Planet. The right ascension is given on pages 78-93 for 0 h of every Green¬ 
wich date. The daily difference appears as a sub notation. By means of the daily 
difference and the known G.G.T. the interpolation for the instant may be made and a 
correction applied to the recorded value of the right ascension for Greenwich 0 hours. 
This interpolation may be made by use of Table IV, pages 112-114 of the Almanac, but as 
this table is arranged for only 12 hours the interpolation may have to be made backward 
from the following day. (Note: The right ascensions of the planets, except Venus, are 
always increasing. At certain periods of some years the right ascension of Venus de¬ 
creases, and the correction for G.G.T. must be applied accordingly.) 

Example: Given the following data, find the hour angle of Venus. Date, 2 January, 1925. a.m. 
Watch 5-13-00, C-W 5-45-05, Chro. slow l m 01 s , Long. 93-47-30 E. 

Watch 5-13-00 

C-W 5-45-05 


Chro. 10-58-05 


Chro. slow 

1-01 



G.C.T. 

R.A.M.O 

Corr. Table III 

22-59-06 1 Jan. 

6-40-30.4 

3-46.5 

R.A.9 2 Jan. 
Cor. IV l h -l m 

16-50-38, Gr. 0 h 

13 (sign reversed) 

R.A.$ 

16-50-25 

G.S.T. 

Long. E. 

5- 43-22.9 (rejecting 24 h ) 

6- 15-10 

L.S.T. 

R.A. $ 

11-58-32.9 

16-50-25 




H.A. 19-08-07.9 


For the Moon. The right ascension of the moon is given in the Nautical Alma¬ 
nac (pages 30-75) for every even hour of Greenwich civil time. Each right ascension 
given is followed by a sub notation of the difference in seconds for the two houi period. 
Table IV may be used for interpolation to find the right ascension at any inter¬ 
mediate period of G.G.T. using the difference for two hours, and the minutes above a 
two hour period, as the arguments at the top of the page and in the left hand column 
respectively. As the table is constructed for only one hour, it will be necessary to 
interpolate backward for time differences of more than one hour. 


Example: Find the local hour angle of the moon at a place whose Long, is 36°-24'-00" W., at the 
instant when the G.C.T. is 18-50-29, 3 January, 1925. 


G.C.T. 18-50-29 3 Jan. R.A.C,18 h 2-11-27 

R.A.M.S. 6-48-23.5 Cor. for 50™-2fr 1-39 (Table IV) 

Cor. Ill 3-05.7 - 

- R.A. (D 2-13-06 

G.S.T. 1-41-58.2 

Long. W. 2-25-36 


L.S.T. 23-16-22.2 

C’s R.A. 2-13-06.0 


C’sH.A. 21-03-16.2 


FINDING THE TIME OF TRANSIT OF A STAR, A PLANET, OR THE MOON. 

21 . As previously explained under apparent time, it is useful for the navigator 
to be able to predict the time of local transit of celestial bodies, for it is at this instant 
that the latitude is most readily and accurately determined. 

For a Star. The Nautical Almanac tabulates, on page 96, the G.G.T. of transit 
at Greenwich of the stars commonly used in navigation. This tabulated time is given 
only to the nearest minute, and for the first day of each month. On page 97 is a table 
of corrections to be applied to find the G.C.T. of Greenwich transit for any other day 
of the month. Having found the G.G.T. of Greenwich transit for the required date, 













TIME. 


17 


the L.C.T. of local transit for that date may be found by applying a correction for the 
local longitude. This correction is a part of the difference in the times of transit for 
the given date and the next succeeding day, as tabulated on page 97, proportional to 
the local longitude, expressed in time, divided by 24 hours. It is to be added for east 
longitudes and subtracted for west longitudes. Having thus found the L.C.T. of local 
transit, apply the longitude in time to obtain the G.C.T. of local transit. Apply to 
this the chronometer error, and obtain the chronometer reading at local transit. Sub¬ 
tract from this the C-W, and the result will be the watch time of local transit. This 
result is correct only to the nearest minute. 

Example: Find the watch time of transit of the star a Virginis (Spica) on 2 January, 1925, at a 
place whose longitude is 67°-30' W., chro. slow l m -06 B , C-W 4-32-19. 

Approx. G.C.T. of Gr. Transit, 1 Jan. 6-40-00 (p. 96, N.A.) 

Cor. for 2 Jan. (-) 04-00 (p. 97, N.A.) 


Approx. G.C.T. of Gr.Transit, 2 Jan. 
Cor. for Long. W., = +4 m x|^ = 

L.C.T. of local transit 
Long. W. 


6-36-00 

45 


6-35-15 

4-30-00 


G.C.T. of local transit 
Chro. error, slow 


11-05-15 

1-06 


Chro. reading at local transit 11-04-09 

C-W (subtract) 4-32-19 


Approx. Watch time of local transit 6-31-50 

The above method gives the watch time of transit correct to the nearest minute. 
This is accurate enough if the altitude of the body at transit is obtained. If, however, 
the altitude at transit is missed, due to clouds, but obtained near transit, the latitude 
may be obtained by a form of meridian altitude sight known as the reduction to the 
meridian. Moreover, the period of twilight when it is dark enough for the stars to be 
clearly discernable, and still light enough for the horizon to be clearly defined, is so 
brief that it is seldom advisable to wait for the transit of the star. It is generally better 
to take the altitude when the conditions of visibility are best for an accurate observa¬ 
tion, and use the method of the reduction to the meridian. This requires an exact 
watch time of transit, which is easily found as follows: 

At the instant of transit the L.S.T. is equal to the body’s right ascension, for the 
hour angle is then zero, and the equation L.S.T. = R.A.-fH.A. becomes L.S.T. = R.A. 
The star’s right ascension may be selected from the Nautical Almanac with only 
an approximate knowledge of the date, and is equal to the L.S.T. at local transit. The 
longitude applied to this will give the G.S.T. at local transit. It is now necessary to fix 
the Greenwich date at local transit. This can be done by finding (from page 96, N.A.) 
the G.C.T. of Greenwich transit for the given date and applying the longitude. For 
the Greenwich date of local transit select the G.S.T. of Greenwich 0 h . Subtract from 
this the G.S.T. of local transit. The result is the period of time, expressed in sidereal 
units, that will have elapsed from Greenwich midnight to the time of local transit. 
Convert this to a mean time interval. The result is the G.C.T. of local transit. 


Example: Solve the last example by the exact method. 


☆’s R.A. = L.S.T. of L.Tr. = 
Long. W. 

13-21-13.5 

4-30-00 

G.C.T. of Gr.Tr. 2 Jan. 
Cor. for Long. W. (—) 

6-36-00 

-45 

G.S.T. of L.Tr. 

G.S.T. of Gr. 0 h (RAMS+ 12) 

17-51-13.5 

6-44-27 

L.C.T. of L.Tr. 2 Jan. 
Long. W. 

6-35-15 

4-30-00 

Sid. Int. 

Cor. Table II (-) 

11-06-46.5 
i 1-49.2 

G.C.T. of L.Tr. 

11-05-15 

G.C.T. of local transit 

Chro. error, slow 

11-04-57.3 

1-06.0 



Chro. reading at L.Tr. 

C-W 

11-03-51.3 

4-32-19 



Watch time of L.Tr. 

6-31-32.3 
















18 


TIME. 


For a Planet. The Nautical Almanac, pages 78-93, gives for each day of the 
year the G.G.T. of Greenwich transit to the nearest minute. From G.C.T. of Green¬ 
wich transit for the given date the L.G.T. of local transit may be obtained by a simple 
interpolation for longitude between the given date and the adjacent date, interpo¬ 
lating forward for west longitude, and backward for east longitude. Then proceed as 
for a star. 


Example: Find the watch time of transit of the planet Venus on 2 January, 1925, at a place 
whose longitude is 67°-45'-45" E., chro. slow l^Oh 9 , C-W 7-29-45. 

Approx. G.C.T. of Gr. Transit, 2 Jan. 10-07-00 
Cor. for longitude (—) 00-11.3 


L.C.T. of local transit 
Long. E. 

G.C.T. of local transit 
Chro. slow 

Chro. reading at L.Tr. 
C-W (subtract) 


10-06-48.7 

4-31-03 


5-35-45.7 (2 Jan.') 
(-) 1-06 


5-34-39.7 

7-29-45 


Approx. Watch time of local transit 10-04-54.7 

If a more exact determination is required it may be had by finding the approxi¬ 
mate G.G.T. of local transit as above, then finding the right ascension of the planet for 
that instant and proceeding as in the exact determination for a star. 

For the Moon. The problem of predicting the time of local transit of the moon 
is similar to that for a planet, but the right ascension changes much more rapidly and 
therefore the daily difference in the G.G.T.’s of Greenwich transits is larger. See pages 
76-77, Nautical Almanac. This requires a more accurate interpolation, which, how¬ 
ever, is facilitated by the use of Table 11, Bowditch, which is self explanatory. 

Example: Find the watch time of local transit of the moon at a place in Long. 23° W.. on 2 Janu¬ 
ary, 1925. Chro. fast l m -59 p , C-W 1-35-15. 

Approx. G.C.T. of Greenwich transit, 2 Jan. 18-38-00 
Cor. for Long. (Table 11, Bowditch) (+) 2-36 


Approx. L.C.T. of local transit 18-40-36 

Long. W. 1-32-00 


Approx. G.C.T. of local transit 20-12-36 

Chro. fast 1-59 


Approx. Chro. reading at local transit 20-14-35 

C-W (subtract) 1-35-15 


Approx. Watch time of local transit 6-39-20 (rejecting 12 h ) 

The exact time of local transit may be found as explained for a planet. 

Note: Since the lunar day is longer than the solar day there are certain dates on which no transit 
of the moon occurs at certain places. 

Example: Find the L.C.T. of transit of the moon at a place in Long. 135° E., on 7 June, 1925. 
G.C.T. of Greenwich transit, 7 June 0M)6 m 
Cor. for Long. 135° E. (Table 11) (-) 23 


L.C.T. of local transit 23-43 6 June 

Since the next transit will not take place for about 24 hours and 50 minutes, it is 
apparent that there will be no transit of the moon at this place on 7 June. 

Again it sometimes happens, when the G.G.T. of Greenwich transit occurs near 
0 h or 24 hours that it is necessary to work from a Greenwich date which differs by one 
from the local date. 

Example: Find the L.C.T. of transit of the moon on 6 June, at a place whose longitude is 60° E 
The Almanac gives no transit of the moon for Greenwich on 6 June, but gives 0 h -06 m as the G C T 
of Greenwich transit on 7 June. 

G.C.T. of Gr. Tr. 7 June, =0 h -06 m = 24M)6 m 6 June 
Cor. for 60° E. Long. ( —) 10 


L.C.T. of local transit 


23-56, 6 June 












CHAPTER II. 

OBSERVATIONS FOR LATITUDE. 


MERIDIAN ALTITUDES. 

, ? 2 * . 7, he ® m ? le s t method of determining latitude at sea by means of observations 

ot celestial bodies is that known as the meridian altitude. In this method the sextant 
altitude of a celestial body is taken when it is on the observer’s meridian and corrected 
to give the true geocentric altitude of the body’s center. This altitude is then com¬ 
bined with the body s decimation to determine the latitude by one of the methods 
explained below, the determination being based upon the fact that the latitude of a 
place is equal to the declination of its zenith, and also to the altitude of the elevated 
celestial pole. Proof: In Figure I let the inner circle represent the terrestial meridian 

of a place, Z', in north latitude, and 
^ the outer circle the celestial meridian. 

E' Q' is the equator, EQ the equi¬ 
noctial. nP and nP' are the celestial 
and terrestial poles. H'R' is the ter¬ 
restial horizon, and NOS the celestial 
horizon to which the altitude of all 
celestial bodies and points are re¬ 
duced. 

Then Z'OQ' is the latitude of the 
place Z'. It is equal to ZOQ, which 
is the declination of the zenith. 

By inspection ZOQ = nPON, the 
altitude of the elevated pole. 

Therefore, the latitude of a place 
is equal to the declination of the zenith 
or the altitude of the elevated pole. 

Figure 1 is not in proportion since 
the celestial sphere is not shown of 
infinite radius as compared to the 
radius of the earth, but as only angles 
measured from the earth’s center are 
considered the deductions are correct. 

When the figure is drawn in proportion, the earth reduces to a point at the center 
of the celestial sphere, as in Figure 2. In this figure a celestial body to be visible must 
be above the horizon, in the unshaded portion. Such 
a body at transit may be on the meridian in either of 
the sectors 1, 2, 3, or 4. 

If it is on the meridian in sectors 1 or 2, it will bear 
toward the depressed pole, i. e.,if the observer is in 
north latitude the body will bear south and vice versa. 

Similarly if the body is in sectors 3 or 4 it will bear 
north from an observer in north latitude and south in 
south latitude. The figure is drawn for north latitude, 
and N and S are the north and south points of the 
horizon. If P represents the south pole N and S will 
be interchanged. 

Denoting the body’s declination by d, its polar 
distance, (90—d), by p, its altitude by H, and its 
zenith distance, (90—H), by Z, we have, if the body 
is in sector 1, 




19 





















20 


OBSERVATIONS FOR LATITUDE. 


Lat. = ZQ = Z—d = (90°—H)—d 
In sector 2, Lat. = ZQ = Z+d= (90°—H)+d 
In sector 3, Lat. = ZQ = PN = H—p = H—(90°—d) 

In sector 4, Lat. = ZQ = PN = H + p = H+(90°—d) 

Therefore the latitude of a place may be determined by observing the sextant alti¬ 
tude of a body at transit, correcting the observed altitude to obtain the geocentric 
altitude of the body’s center, selecting the body’s declination from the Nautical Alma¬ 
nac, and combining the altitude and declination in accordance with that one of the 
above equations which fits the case. 


FINDING THE DECLINATION. 


23. The declination of the sun is tabulated in the Nautical Almanac with the 
equation of time, and the method of selecting it for any given instant of G.C.T. is the 
same as that already explained for the latter. 

The declinations of the moon, of the planets, and of the stars are tabulated with 
their right ascensions and the method of selecting them for any instant of G.C.T. is the 
same as that already explained for the latter. 

For the meridian altitude of the sun, the moon, or a planet, the declination should 
be selected for the G.C.T. of the time of transit. The declination of a star changes so 
slowly that it may be selected for the nearest first of the month without correction. 

24. In the examples standard symbols for altitude will be used as follows: 

h s , the altitude as observed with the sextant. 

h, the sextant altitude corrected for I.C. 

H 0 , the sextant altitude with all corrections applied, that is the true geocentric 
altitude of the center. 

H c , the calculated geocentric altitude of the center. 

H a , the approximate altitude. 

Note. —As an exercise, in the following examples and problems, the longitude at time of sight is 
given, and the watch time at which the sight is to be taken is required. The problems, therefore, 
simulate the solution for latitude for a ship on a north or south course, (with an unchanging longitude). 
Practically, when underway with a changing longitude, one of the following methods is preferable. 

(a) For the sun. To determine the W.T. of transit by Todd’s method, to be explained hereafter. 

(b) For any other body. To use the prospective longitude at time of sight as in the above prob¬ 
lems, to determine the prospective W.T. of transit. Then to take the observation at about that watch 
time, choosing, however, the instant of best visibility, steadiness of the ship, etc. The actual watch 
time of sight is then noted and used in the solution, the D.R. longitude for that instant determined, 
and the body’s “t” determined, by the method of Art. 20. The solution will then be either by the 
method of meridian altitude, or reduction to the meridian, according as “t” is, or is not, zero. 

Example: At sea, 2 January, 1925, the noon position by D. R. is Lat. 33°—19' N., Long. 45°-T7' W. 
The navigator observes the sun at L.A.N. bearing south, as follows. h s 33°-35'-30", I.C. (—) l'-OO", 
height of eye, 31 feet, C-W 3—03—09, chro. slow l m -04.9 s . Find the W.T. of L.A.N. and the latitude by 
observation. 

MERIDIAN ALTITUDE, SUN. 


2 Jan., 1925, L.A.N. 


Sun. 



M 


L.A.T. of L.A.N. 

X (W) 

G.A.T. of L.A.N. 

Eq.T. (sign reversed) (+) 4-07 

G.C.T. of L.A.N. 

Chro. slow 


15-05-15 (2 Jan.) 

1-04.9 


C.T. of L.A.N. 
C-W (subtract) 
W.T. of L.A.N. 


15-04-10.1 

3-03-09 

12 - 01 - 01.1 


12-00-00 (2 Jan.) 

3-01-08 


15-01-08 (2 Jan.) 



L=Z 


Lat. 33°-19' N. 

X 45°-17' W. 

3h—01 m —08 s 
d=90°—(Ho+d) 


Cor. (+) 8-32 

Ho 33-44-02 Sub. 

d 22-55-48 Cor. 

Ho+d 56-39-50 dec. 

90— (Ho + d) 33-20-10 N. Cor. 

=Lat. d 


I.C. (-) 1-00 
T. 46 ( + ) 9-14 


+ 0-18 
(+) 8-32 

22-56.0 S. 
-2 

22-55.8 S. 


H.D. 

Int. 


(-) 


O'.2 
1.1 


Eq.T. (-) 4 m -05*.8 
Cor. (+) 1.2 

Eq.T. 4-07.0 
H.D. (+) TT 
Int. 1 

Cor. (+) 1.2 


Cor. (-) 


.22 














OBSERVATIONS FOR LATITUDE. 


21 


Example: At sea, 4 July, 1925, p.m., in D.R. Lat. 37°-53' N., Long. 59°-24'30" W., the navigator 
of a vessel observed the planet Venus on the meridian for latitude. The data were as follows: C-W 
4-05-27, chro. fast 6 m -02 s , I.C. (+) l'-OO", height of eye 36 feet, h s 73-29-00. Find (a) the approxi¬ 
mate G.C.T. of local transit, (b) the exact W.T. of local transit, (c) the approximate altitude at transit 
to be used as an aid in finding the planet in daylight, (d) the latitude at time of transit. 


4 July, 1925, P.M. 





MERIDIAN ALTITUDE, PLANET. 


Venus. 



D.R. Lat. 37°-53' N. 

X 59°-24'-30" W. 

= 3 h -57 ra -38» 

L=z + d=90 —H o +d=90+d —Ho 
Ha=90+d-L 


Ap. G.C.T. of Gr.Tr. 
Cor. for X ( + ) 

13-27-00 

0-10 

(4 July) 



+ 

ca¬ 

ll 


111-17-12 

37-53-00 

L.C.T. of L.Tr. 

X (W) 

13-27-10 

3-57-38 




Ha 


7Q__ 24_ 1 o 






Ap. G.C.T. of L.Tr. 

17-24-48 

(4 July) 

R.A. 

Cor. 

8-12-05 
(+) 3-43 

Dec. 

Cor. 


21-28.2 

11.0 

R.A.=L.S.T. of L.Tr. 

8-15-48 


R.A. 

8-15-48 

d 


21-17.2 

X (W) 

3-57-38 


D.D. 

307" 

D.D. 


152" 

G.S.T. of L.Tr. 

12-13-26 


Int. 

17. h 41 

Int. 


17. h 41 

R.A.M.S. + 12 

18-45-56.5 


Cor. 

3'-43" (T. IV) 

Cor. 


1 l'-OO" 

Sid. Int. 

II 

17-27-29.5 

2-51.6 


h s 

73-29-00 

I.C. 

(+) 

l'-OO" 

G.C.T. 

17-24-37.9 


Cor. 

(-) 5-11 

T. 46 

(-) 

6-11 

Chro. fast 

6-02 


Ho 

73-23-49 

Cor. 

(-) 

5-11 

Chro. T. of L.Tr. 

17-30-39.9 


90+d 

111-17-12 




C-W (subtract) 

4-05-27 


90+d-H o 

37-53-23 N. 




W.T. t>f L.Tr. 

13-25-12.9 

or 


=Lat. 





lh-25m-12.9 8 


\ 























22 


OBSERVATIONS FOR LATITUDE. 


Example: At sea, 2 May, 1925, p.m., in D.R. position Lat. 7°-18' N., Long. 61°-23' E., observed 
the meridian altitude of the moon’s upper limb bearing north as follows: C-W 7-54-47, chro. fast 
2 m -19 8 , h s 83°-54', I.C. (+) 2'-00", height of eye 28 feet. 

Required: The approximate G.C.T. of local transit, the exact watch time of the moon’s transit, 
and the latitude at time of eight. 


2 May, 1925, P.M. 

7n 


MERIDIAN ALTITUDE, MOON. 
Moon. 



Ap. G.C.T. 01 Gr.Tr. 
Cor., X, E. (T. 11) 

Ap. L.C.T. of L.Tr. 

X (E.) 



Lat. 7°-18' N. 

X 61°-23' E. 

4 h -05 m 32 s 

L=d — z =d — (90 — Ho) 
=d + H o -90 


19-32-00 
(-) 08-00 


(2 May) 


19-24-00 

4-05-32 


Ap. G.C.T.Q of QL.Tr. 

C’s R.A.=L.S T. of L.Tr. 

15-18-28 (2 May) 

10-04-15 

R.A. 

Cor. 

(+) 

10-01-36 

2-39 

Dec. ( + ) 

Cor. (-) 

13-48.8 H. 

10.7 

X (E.) 

4-05-32 

R.A. 


10-04-15 

d 

13-38.1 

G.S.T. of L.Tr. 

5-58-43 

Dif. 2 Hrs. 

243" 

Dif. 2 Hrs. (- 

-) 16'.4 

R.A.M.S. + 12 

14-37-33.4 

1 Hr. 

2'-01".5 

1 

8'.2 

Sid. Int. 

15-21-09.6 

18.5 

m. 

37'.5 

18.5 m. 

2.5 (T. IV) 

Table II 

2-30.9 

Cor. 

(+) 

2'-39".0 

Cor. (-) 

10.7 

G.C.T. of L.Tr. 

Chro. fast 

15-18-38.7 

2-19 

h 8 

I.C. 

(+) 

83-54-00 

2-00 

T. 49 (-) 

Eye (+) 

15-00 

0-37 

Chro. T. of L.Tr. 

C-W (subtract) 

15-20-57.7 

7-54-47.0 

h 

Cor. 


83-56-00 

14-23 

Cor. (-) 

14-23 

W.T. of L.Tr. 

7-26-10.7 

Ho 

d 


83-41-37 

13-38-06 





Ho+d 

97-19-43 
(-) 90-00-00 





Lat. 


7-19-43 N. 




H.P.=55'.2 


Example: At sea, 2 January, 1925, p.m., D.R. position Lat. 51°-13 / N., Long. 19°-30' W., 
observed the star a Ursae Major (Dubhe) at lower transit bearing north, as follows- C-W 1-18-19 
chro. fast 1*M)L9 8 , I.C. (+) 1-30", height of eye 36 feet, h s 23°-27'-00". Find watch time of lower 
transit, and the latitude. 


2 Jan., 1925, P.M. 

-m. 



MERIDIAN ALTITUDE, STAR, LOWER TRANSIT. 
Dubhe. 



Lat. 51°-13' N. 

X 19°-30' W. 

lh— 18 m — 00 a 

L=Ho+p=90+H o -d 


































OBSERVATIONS FOR LATITUDE. 23 


*’s R.A. 

10-59-06.5 

Dec. 

62-09.1 N. 



Plus 

12-00-00 

hs 

23-27-00 

I.C. 

+ l'-30" 

L.S.T. of L.Tr. 

22-59-06.5 

Cor. 

(-) 6-36 

T. 46 

(_) fj-06 

X(W.) 

1-18-00.0 

Ho 

23-20-24 

Cor. 

(-) 6-36 

G.S.T. of L.Tr. 
R.A.M.S. + 12 

24-17-06.5 

6-44-27.0 

90+ Ho 

d 

113-20-24 
(-) 62-09-06 



Sid. Int. 

II 

17-32-39.5 
(-) 2-52.4 

Lat. 

51°-11'-18" N. 



G.C.T. of L.Tr. 
Chro. fast 

17-29-47.1 

1-01.9 





Chro. T. of L.T. 
C-W 

17-30-49.0 

1-18-19 





W.T. of L.Tr. 

4-12-30 p.m. 






Example: The navigator of the U.S.S. Birmingham in D.R. position, Lat. 60°-15' S., Long. 
55°-50'-30" E., at about 4:07 p.m., on 1 May, 1925, observes the star Sirius on the meridian as follows: 
C-W 8-01-15, chro. slow 14 m -25 8 , h s 46°-25 / -00", I.C. (+) l'-30", height of eye 45 feet. Find the 
watch time of transit and the latitude. 


1 May, 1925, P.M. 


MERIDIAN ALTITUDE, STAR 
Sirius 



R.A.=L.S.T. of L.Tr. 

6-41-49.8 

d = 

16-37 S. 



X (E.) 

3-43-22 

h s 

46-25-00 

I.C. 

(+) 1-30 

G.S.T. 

2-58-27.8 

Cor. 

(-) 6-01 

T. 46 

(-) 7-31 

R.A.M.S. + 12 

14-33-36.9 

Ho 

46-18-59 

Cor. 

(-) 6-01 

Sid. Int. 

12-24-50.9 

90 + d 

106-37-00 



Tab. II 

2-02 

Lat. 

60-18-01 S. 



G.C.T. of L.Tr. 

Chro. slow 

9 

12-22-48.9 (1 May) 
14-25 





C.T. of L.T. 

C-W 

12-08-23.9 

8-01-15 






W.T. of L.Tr. 


4-07-08.9 

























24 


OBSERVATIONS FOR LATITUDE. 


REDUCTION TO THE MERIDIAN. 

25. It sometimes happens that a body is obscured by clouds at the instant of 
transit. In this case, should it be possible to observe the altitude shortly before or 
alter transit, the altitude then taken may be corrected, by the method hereafter ex¬ 
plained, to obtain the meridian altitude. The method is called the reduction to the 
meridian. 

. The paths in which the celestial bodies appear to move are curves which reach 
their highest point on the observer’s meridian. For a small angular distance on either 
side ol the meridian these curves are nearly parallel to the observer’s horizon, and 
consequently as a body moves in its curve near the meridian its change of altitude is 
relatively slow* While during this period the change in altitude is relatively slow, it is 
still appreciable and will vary in rate depending on the relation between the observer’s 
latitude and the body’s declination. Thus a body which transits high above the 
observer s horizon will change its altitude more rapidly than one which transits at a 
low altitude. For the various combinations of the observer’s latitude and declinations 
ot celestial bodies the changes of altitude which will occur while a body is changing its 
hour angle fifteen minutes of arc, either immediately before or immediately after 
meridian passage, have been computed and are tabulated in Table 26, Bowditch. In 
computation these tabulated values are designated as “a.” 

For the sun a change of hour angle of 15 minutes of arc will take place in one 
mm i! t j ° f a PP are . nt ti me > an d for a star in one minute of sidereal time. Since the 
method ol reduction to the meridian is used for small changes of hour angle only, the 
dilierence between an apparent time interval and a mean time interval will be inappre¬ 
ciable, and the tabulated values of “a” may be used for mean time minutes without 
material error. Similarly, in the case of a planet, the change of right ascension during 
the period it is close to the meridian is so small that such change may be neglected, and 
minutes of sidereal time may be used for a planet for the tabulated values of “a ” 

It may be proved by mathematics that if a body changes its altitude “a” seconds 
while changing its hour angle one minute of time from the meridian, then, in any 
other small period, say,, t minutes of time, within the limits of slow movement in 
altitude, it will change its altitude “at 2 ” seconds of arc. Hence, knowing the time of 
transit ot a body and the time of observations near transit, we may find the altitude 
at transit by applying “at 2 ” seconds to the observed altitude. 

To find “t. For the sun the difference between the computed watch time of noon 
and the watch time of observation is sufficiently accurate to use as “t.” For a star or a 
planet, d the watch time of transit has been computed by the exact method, the differ¬ 
ence between the watch time of transit and observation may be reduced to a sidereal 
interval and used as “t.” Or, if the exact watch time of transit has not been computed 
the watch time of observation should be converted to L.S.T. The difference between 
the L.S. I and the body s R.A. is the “t” required. This latter method should always 
be used for moon sights, because the changes of R.A. and declination of the moon are 
so rapid that they must be corrected for the G.G.T. of the instant of observation. 

lo hnd a. Table 26 tabulates the values of “a” for latitudes from 0° to 60° 
combined with declinations from 0° to 63°, thus including the usually navigated waters 
and the principal celestial bodies used in navigation. Values are omitted for those cases 
in which the altitude of the body at transit is more than 86° or less than 6°, as results 
are inaccurate in those cases. 

, T ° £ lad ,“ atV ’ .The values of “at 2 ” are tabulated in Table 27, Bowditch, for those 
yaiues of a and t for which the method is sufficiently accurate. The correction 
is additive to altitudes observed near upper transit, and subtractive from altitudes 
observed near lower transit. 

Having found the meridian altitude by applying “at 2 ” to an altitude observed 
near transit, the latitude is found as explained for meridian altitudes. The resultant 
latitude, however is the latitude of the place of observation. In the case of a reduction 
t( ?.. ™ en( ffan of the sun the latitude should be corrected for the run from noon to 
obtain the noon latitude. 


OBSERVATIONS FOR LATITUDE. 


25 


Example: A destroyer is steaming north (true) at 20 knots. At 12 minutes before L.A.N. an 
altitude of the sun is taken. The latitude obtained by the method of reduction to the meridian is 
found to be 30°-10' N. This is the latitude of the place where the observation was taken. At L.A.N. 
the destroyer will be four miles north of that place. Therefore, the latitude at L.A.N. will be 30°-14' N. 

VALUE OF THE DECLINATION TO BE USED IN A REDUCTION TO THE MERIDIAN. 

26. In working a reduction to the meridian, the declination should properly be 
selected for the G.C.T. of the observation. This is necessary for the moon because of 
its rapid change of declination, but for the other bodies it is sufficiently accurate to use 
the declination for the G.C.T. of transit. 

Example: On 3 July, 1925, in D.R. position Lat. 12°-44' N., Long. 30°-14'-45" W., the navigator 
observes the sun for latitude, bearing north, as follows: W ll h -55 m -21 s , C-W 2 h -05 m -10 s , chro. fast 
4 m -15 a , I.C. (+) 2'-00", height of eye 28 feet. h s 79°-20'-15". Find the latitude at time of sight. 
If, after the observation, the ship continues on her course and speed which are 15° true at 15 knots, 
what will be the latitude at L.A.N.? 


REDUCTION TO THE MERIDIAN, SUN. 


3 July, 1925, A.M. 


Sun. 





O 

r- 

_ — 

Z Q 




6 /^ 

/ \ 

: \ p 

r 


I7\ 


Lat. 12°-44' 

N. 

/ \ 

\ 

1 N 1 



L i s 


X 30°-14'-45" W. 


\ J N 1 

i 

7 

s 


= 2 h -00 m - 

-59* 




/ 

y 

Lat. 

=d —z=d— (90 —H 0 ) 

i=H o +d-90 

b 


E 

1 — 





L.A.T. of L.A.N. 
X (W.) 

12 -00-00 

2-00-59 

h s 

Cor. 

79-20-15 
( + ) 12-26 

T. 46 
I.C. 

(+) 10'-40" 

(+) 2'-00 


G.A.T. of L A.N. 

14-00-59 

Ho 


79-32-41 

Sub. 

(-) 0-14 

Eq.T. (-) 3-57.1 

Eq.T. (sign reversed) (+) 3-57.1 

at 2 


12-24 

Cor. 

(+) 12-26 

Cor. 00 

G.C.T. of L.A.N. 

14-04-56.1 

He 


79-45-05 

O’s d 

22-59. IN 

Eq. T. 3-57.1 

Chro. fast 

4-15 

d 


22-59-06 

Cor. 

0.0 

H.D. 0.5 

Chro. T. of L.A.N. 2-09-11.1 

Ho+d 


102-44-11 

d 

22-59.IN 

Int. 0.0 

C-W (subtract) 

2-05-10 

(-) 


90-00-00 

H.D. 

0.2 

Cor. 0.0 

W.T. of L.A.N. 

12-04-01.1 

Lat. 


12-44-11 

Int. 

.1 


W.T. of Obs. 

11-55-21 

A L. 


2-06 

Cor. 

.02 


t 

a 

at 2 

8-40.1 

Q Q 

12'-24" 

Lat. at L. A.N. 12-46-17 N. 


























26 


OBSERVATIONS FOR LATITUDE. 


Example: At about 7:30 p.m., 3 July, 1925, in Lat. 25°-40' N., and Long. 46°-50' W., the navi¬ 
gator observes the planet Saturn bearing south as follows: W T^O^O 8 , C-W 2 b -59 m -20 s , chro. slow 
0 m -50 8 , planet’s h s 52°-30'-00", I.C. 0'-00", height of eye 30 feet. Find latitude at time of sight by 
reduction to meridian. 


3 July, 1925, P.M. 

<v> 


REDUCTION TO THE MERIDIAN, PLANET. 
Saturn. 




Lat. 25°-40' N. 

X 46°-50' W. 

3 h -07 m -20 s 

L =z — d 

=90 - H„ - d =90 - (Ho+d) 


W 

C-W 

Chro. 

Chro. slow 

G.C.T. 

R.A.M.S. + 12 

Table III 

G.S.T. 

Long. (W.) 

L.S.T. 

R.A. b 


7-30-30 

2- 59-20 

10-29-50 

0-50 

22-30-40 (3 July) 

18-41-59.9 

3-41.9 

17-16-21.8 

3- 07-20.0 


14-09-01.8 

14-24-32.2 


15-30.4 E. 

2".9 

ll'-37" 


hs 

Cor. 


H„ 

at 2 


52-30-00 
(-) 6-07 


52-23-53 
( + ) 11-37 


H c + d 


Lat. 


I.C. 
T. 46 


Cor. 


(-) 


0-00 

6-07 


(-) 


52-35-30 

11-44-42 

64-20-12 

90-00-00 

25-39-48N 


b’s Dec. 
Cor. (-) 

d 

D.D. 

Int. 

Cor. 


11-44.8 S. 
0.1 


(-) 


0.1 

22 h .5 


(-) 


R.A. 14-24-35 
Cor. (-) 02.8 


R.A. V 
D.D. (-T 
Int. 

Cor. (-) 


3" 
22 h .5 
2".8 


THE CONSTANT. 


27. The four equations for latitude by the method of meridian altitudes are: 

L = (90—H 0 )—d; L = (90—H 0 ) -fd; L = H 0 — (90—d); L = H 0 + (90—d) 

_ Letting c equal the algebraic sum of the I.C. and the correction from Table 46 
Bowditch, and substituting (h s -f-c) for H 0 , these equations become: 


L = 90— (h 8 +c)—d = (90—c—d)—h s 
L = 90 (h s +c)+d= (90—c+d)—h s 

L = h s +c— (90—d) = h s — (90—d—c) 
L = b s +c+(90—d) = h 8 + (90—d+c) 


In the latter forms of the equations, the quantities within the brackets may be 
computed in advance of the observation and are called constants. The computation 
in advance is accomplished as follows for observations of the sun, for which body the 
method is principally used: 

, F + L St k T Th ® G ; G * , l r - ° f L is com Puted, and the declination of the sun selected 
within tL N brackets A manaC ** ^ time ' ThiS gWeS ° ne ° f the unknown quantities 

Second. The time of L.A.N. being known, the D.R. latitude for noon may be pre¬ 
dicted. 1 his D. K. latitude and the declination as found above are substituted in the 
equation for latitude and the equation solved for the approximate altitude at noon. 
tor this approximate altitude the correction for altitude is selected from Table 46 
Bowditch, the height of eye from which the noon observation is to be taken, the calcu¬ 
lated approximate altitude, and the date being the arguments used. With this cor¬ 
rection from Table 46, is combined the I.C. of the sextant which will be used for the 
observation, the result being c With c and d known, the constant may be computed. 

When the constant is found as above, the noon latitude may be found immediately 
alter the sextant altitude at noon is obtained, by simply combining the sextant altitude 
and the constant. The manner in which they are combined will depend on which one 
ol the lour equations governs the case. 






















OBSERVATIONS FOR LATITUDE. 


27 


Example: At sea, 1 January, 1925, the predicted L.A.N. position of a ship is Lat. 42°-20' N., 
Long. 42°-27'W., the navigator observes the sun on the the meridian for latitude as follows: C-W 
7 * ™ 5, f hro * slow lm_14s ’ LG - (“) I'-OO", height of eye 20 feet, h s 24°-23'-00". Find the W.T. of 
L.A.N., the noon constant (K n ) and the latitude. 

CONSTANT FOR MERIDIAN ALTITUDE, SUN. 

1 Jan., 1925, LAN. Sun. 

Z 

Lat. 42°-20' N. 

X 42°-27' W. 

= 2 h -49 m -48 sl 

L=z —d=(90 —Ho) — d 
=90 — (hs+c) — d, K=90-(c+d) 
H a =90 —L —d=90 — (L-f d) 

N 


L.A.T. of L.A.N. 

X (W.) 

12-00-00 

2-49-48 




d 

L 


23-00.9 

42-20 

I.C. (-) 1-00 

T. 46 (+) 9-39 

G.A.T. of L.A.N. 

14-49-48 (1 Jan.) 

Eq.T. 

(—) 

3-37.5 

L + d 


65-20.9 

Sub. (+), 0-18 

Eq.T. (sign reversed) (+) 3-38.5 

Cor. 

(-) 

1.0 

Ha 


24-39.1 

Cor. (+) 8-57 

G.C.T. of L.A.N. 

14-53-26.5 (1 Jan.) 

Eq.T. 

(-) 

3-38.5 

Dec. 


23-01.1 (S) 

d 

23-00-54 

Chro. slow ( — 

•) 1-14 

H.D. 


1.2 

Cor. 

(-) 

0.2 

d+c 

23-09-51 

Chro. T. of L.A.N. 

14-52-12.5 

Int. 


.8 

d 


23-00.9 (S) 

K n 

66-50-09 

C-W (subtract) 

2-48-35 

Cor. 


1.0 

H.D. 

(-) 

0.2 

hs 

24-23-00 

W.T. of L.A.N. 

12-03-37.5 




Int. 


.9 

Lat. 

42-27-09 N 






Cor. 

(-) 

0.2 

. 



28. A constant may also be computed in advance of observation for a given 
interval before local apparent noon, using the method of the reduction to the meridian. 
In this case the reduction at 2 must be computed, finding a from the known approximate 
latitude and the declination. To avoid interpolation “t” is selected as an even number 
of minutes. The sextant altitude observed at the selected time, when applied to this 
constant gives the latitude at time of sight. The constant may be altered to give the 
noon latitude by applying the run in latitude for the interval to noon. 




















28 


OBSERVATIONS FOR LATITUDE. 


Example: On 2 January, 1925, a navigator predicts the noon D.R. position to be Lat. 22°-15'- 
30" N., Long. 44°-02'-18" W. He decides to prepare a constant for use at 12 minutes before L.A.N. 
and obtains the following data: C-W 2-51-10, chro. slow lO 1 "-^ 8 , I.G. (+) 1-00", height of eye 42 
feet. Find W.T. of L.A.N., W.T. of observation, and work out constant. At time of observation h s is 
44°-40'-15". Find latitude at time of sight. If the vessel is on course 20° true, speed 10 knots, what 
was latitude at L.A.N.? 


2 Jan., 1925, A.M. 


CONSTANT FOR REDUCTION TO THE MERIDIAN, SUN. 
Sun. 


■Vrv 




Lat. 22°-15'-30" N. 

X 44°-02'-18" W. 

= 2 h -56 m -09 s .2 

L =z — d =90 — (h a +c) — d 
K n =90 —c —d, Kr=Ku — at 2 
H a =90 — L — d =90 — (L + d) 


M 


L.A.T. of L.A.N. 

X (W.) 

12-00-00 

2-56-09.2 

L 

d 


22°-15'.5 

22 -55 .8 

I.C. 

T. 46 

(+) 

(+) 

1-00 

8-46 



G.A.T. of L.A.N. 

14-56-09.2 (2 Jan.) 

L + d 


45- 11.3 

Sub. 

(+) 

0-18 

Eq.T. 

(-) 4-05.8 

Eq.T. (sign reversed) 

(+) 4-06.9 



90°-00' 

Cor. 

(+) 

10-04 

Cor. 

(+) 1.1 

G.C.T. of L.A.N. 

15-00-16.1 (2 Jan.) 

H a 


44°-48'.7 

Dec. 


22-56.0 

Eq.T. 

(-) 4-06.9 

Chro. slow ( —) 

10-18.0 




Cor. 

(-) 

0.2 

H.D. 

1.2 

Chro. T. of L.A.N. 

14-49-58.1 



90-00-00 

d 


22-55.8 

Int. 

.9 

C-W (subtract) 

2-51-10 

d 


22-55-48 

H.D. 


0.2 

Cor. 

1.08 

W.T. of L.A.N. 

11-58-48.1 

90 —d 


67-04-12 

Int. 


1 



W.T. of Obs. 

11-46-48 

Cor. 

(-) 

10-04 

Cor. 


0.2 



t 

L=22.3 N. \ a =2" 
d=22.9S. / at 2 =5'- 

12-00.1 

’ 4 

Kn 

at 2 


66-54-08 

5-46 






-46" 

Kr 

hs 


66-48-22 

44-40-15 






C 20° Dist. 2 miles 


Lat. 

A L 

(+) 

22-08-07 N. 
1-54 N. 








Lat. 


22-10-01 N. 







29. It is usual to combine both of the preceding methods, that is, the navigator 
computes in advance a series of constants one of which is to be used for the altitude at 
transit if obtained, and the others at certain intervals before transit. The intervals 
before noon are usually taken as a regular series, differing from each other by a uniform 
number of minutes, usually from two to five minutes. Having computed this series of 
constants the navigator begins to observe the sun’s altitude shortly before the watch 
time for which the first constant has been computed. He takes the altitude of the sun 
at the watch time of the first constant and predicts the noon latitude. He then again 
observes the sextant altitude of the sun at the watch time of each of the other constants 
and at Local Apparent Noon, and applies these altitudes to the corresponding con¬ 
stants. The resulting latitudes in all cases should be about the same. Should any of 
the observations be lost, due to clouds, the result of the other observations give the 
navigator the noon latitude. The closeness with which the various results agree, gives 
a check on the accuracy of the observations and computations. 

The following is quoted from Bowditch: 


“A common practice at sea is to commence observing the altitude of the sun’s lower limb above 
the sea horizon about 10 minutes before noon, and then, by moving the tangent-screw, to follow the 
sun as long as it rises; as soon as the highest altitude is reached, the sun begins to fall and the lower 
limb will appear to dip. When the sun dips the reading of the limb is taken, and this is regarded as 
the meridian observation. 

“It will, however, be found more convenient, and frequently more accurate, for the observer to 
have his watch set for the local apparent time of the prospective noon longitude, or to know the error 
of the watch thereon, and to regard as the meridian altitude that one which is observed when the watch 
indicates noon. This will save time and try the patience less, for when the sun transits at a low alti¬ 
tude it may remain ‘on a stand,’ without appreciable decrease of altitude for several minutes after 






















OBSERVATIONS FOR LATITUDE. 


29 


noon; moreover, this method contributes to accuracy, for when the conditions are such that the motion 
m altitude due to change of hour angle is a slow one, the motion therein due to change of the observer’s 
latitude may he very material, and thus have considerable influence on the time of the sun’s dipping. 
This error is large enough to take account of in a fast moving vessel making a course in which there is 
a good deal of northing or southing. 

“In observing the altitude of any other heavenly body than the sun, the watch time of transit 
should previously be computed and the meridian altitude taken by time rather than by the dip. This 
is especially important with the moon, whose rapid motion in declination may introduce still another 
element of inaccuracy.” 

The method of accurately determining the noon D.R. longitude involves the 
determination of the sun’s hour angle by observation at some time during the forenoon, 
and will be explained in a later chapter. 

Example: In the forenoon of 2 July, 1925, a ship is steammg at 15 knots on course 33° true. The 
navigator has predicted the position at local apparent noon to be, Lat. 38°-24' N., Long. 24°-10' W. 
He decides to prepare constants for use with reduction to the meridian of the sun, and to take observa¬ 
tions every 4 minutes, beginning 12 minutes before L.A.N. Given the following data, find the W.T. 
of L.A.N., the time at which each observation for reduction to the meridian is to be taken, and the 
constants, taking account of the run in latitude from the time of observation to L.A.N. The I.C. of 
the sextant is (+) l'-OO", height of eye 32 feet, chro. slow l^Ol^ 8 , C-W 2-14-17. If the sextant 
altitudes of the sun observed at 4 minute intervals before L.A.N. and at L.A.N. are 74°-18 / -15", 
74°-24'-30", 74°-27 / -45", and 74°-28'-30", find the noon latitudes. 


CONSTANT FOR A SERIES OF REDUCTIONS TO THE MERIDIAN. 


2 July, 1925, L.A.N. 



Sun. 



Lat. 38°-24' N. 

X 24°-10' W. 

= l h 36 m -40 8 

L=d+z=d+90-H o =d+90- (h a -f-C) 
K n =d+90 — C. H a =d+90— L. 


L.A.T. of L.A.N. 12-00-00 

X (W.) 1-36-40 


G.A.T. of L.A.N. 

13-36-40 (2 July) 

Eq.T. 

(-) 3-44.9 



Eq.T. (sign reversed) (+) 3-45.7 


Cor. 

(+) 0.8 



G.C.T. of L.A.N. 

13-40-25.7 (2 July) 

Eq.T. 

(-) 3-45.7 


Dec. 

Chro. slow 

1-01.7 


H.D. 

(+) 0.5 


Cor. 

Chro. at L.A.N. 

13-39-24.0 


Int. 

1.6 


d 

C-W (subtract) 

2-14-17 


Cor. 

(+) 0.8 


H.D. 

W.T. of L.A.N. 

11-25-07 





Int. 

L 38°-24' N., d 23°-03'.7 N., a =5.3" 





Cor. 

90 + d 

113-03-42 

at 2 


1-25 



Cor. ( 

-) 10-58 






Kn 

112-52-44 

K„ 


112-52-44 

K„ 




k 4 


112 51-19 

Kg 


fas 

74-28-30 

hs4 


74-27-45 

hs 8 


Lat. at sight 

38-24-14 N. 


* 

38-23-34 N. 



Course. 33°, Dist., 1, 

2, 3, mi. 

A L 


0-48 N. 



Lat. at L.A.N. 

38-24-14 N. 



38-24-22 N. 




90-00 




d 

23-03.7 



90 + d 

L 

113-03.7 

38-24 


23-04.0 N. 

Ha 

74-39.7 

(-) 

0.3 

T. 46 (+) 

10-12 


23-03.7 N. 

Sub. ( —) 

0-14 

(-) 

0.2 

I.C. (+) 

1-00 


1.7 

Cor. (+) 

10-58 


.3 


5-39 


12-43 

112-52-44 

K„ 

112-52-44 

112 47-05 

k 12 

112-40-01 

74-24-30 

hs !2 

74-18-15 

38-22-35 N. 


38-21-46 N. 

1-42 N. 


2-30 N. 

38-24-17 N. 


38-24-16 N. 


LATITUDE BY OBSERVATION OF POLARIS. 


30. The latitude of a place is equal to the altitude of the elevated pole. There¬ 
fore if the north star, Polaris, were exactly at the north pole, its corrected observed 
altitude would be equal to the latitude, and in the northern hemisphere the latitude 
could be directly obtained by observing the altitude of Polaris. However, Polaris is 
not exactly at the north pole, its polar distance (in 1925) being about l°-06'. 
It therefore moves about the pole, as do the other stars, in a diurnal circle, which, 

































30 


OBSERVATIONS FOR LATITUDE. 



Fig. 3 



proper sign for application to the 


however, is comparatively very small, and it 
transits the upper and lower branches of the 
meridian each sidereal day. Let Figure 3 repre¬ 
sent the meridian of a place, and a and b the 
positions of Polaris at upper and lower transits. 
When the star is at a, the latitude is equal to 
the observed altitude, aON, minus the polar 
distance, aOP, and when the star is at b, the 
latitude is equal to the observed altitude plus the 
polar distance. 

In Figure 4, let ZPN represent the meridian as 
seen from 0, Figure 3, P the north pole, and 
c d e f the small diurnal circle of Polaris. Since 
the diurnal circle of Polaris is relatively small 
the following proof is approximately correct and 
gives results accurate enough for the practical 
navigator. If Polaris is at any position c, not 
on the meridian, its altitude will differ from the 
altitude of the elevated pole by xP. Let t be the 
hour angle of Polaris, p its polar distance. The 
n xP = p cos t. By the same method the difference 
between the altitude of the pole and of Polaris 
may be shown to be p cos t for any other position 
of Polaris, such as d, e, and f. 

The values of p cos t have been computed for 
every ten minutes of the observer’s local sidereal 
time and are tabulated in Table I of the Nautical 
Almanac, and may be determined for any other 
instants of L.S.T. by a simple interpolation. 
The tabulated values are accompanied by the 
observed altitude. 


Example: At W.T. 6-32-15 a.m., 2 January, 1925, the navigator of the U.S.S. Mississippi in Lat. 
30°-27'-16" N., Long. 134°-18'-22" W., observed the star Polaris for latitude as follows: C-W 8-51-12, 
chro. slow 6 m -02 s , I.C. (+) 2'-00", height of eye 40 feet, h s 29°-30'-15 // . Find latitude. 

W.T. 6-32-15 h 8 29-30-15 

C-W 8-51-12 I.C. + 2-00 


Chro. 15-23-27 

Chro. slow 6-02 


29-32-15 
T. 46 (-) 7-55 


G.C.T. 

R.A.M.O+12 

III 

G.S.T. 

Long. 


15-29-29 (2 Jan.) 

6-44-27.0 
2-32.7 


22-16-28.7 
8-57-13.5 W. 


H 0 29-24-20 

Cor. Tab. I 1-05-30 


Lat. 30-29-50 


L.S.T. 13-19-15.2 


Given the data below find the W.T. of transit and the latitude by observation 
at transit. 



Problem 1 

Problem 2 

Problem 3 

Problem 4 

Body 

Sun 

Sun 

Moon 

Moon 

Date 

2 Jan., 1925 

2 May, 1925 

2 July, 1925 

2 Jan., 1925 

D.R. Lat. 

33-08 S. 

38-16 N. 

50-01 N. 

34-40 S. 

D.R. Long. 

45-17 W. 

72-10-25 W. 

167-00 E. 

54-04-00 W. 

C-W 

3-03-09 

4-52-16 

1-56-04 

3-26-42 

Chro. error 

slow l m -04.9 s 

fast 3 “-54 s 

fast 56 m -19 s 

slow 32 m -17 s 

I.C. 

(-) l'-OO" 

(+) r-30" 

(+) l'-30" 

0-00 

Ht. of eye 

31 feet 

40 feet 

40 feet 

36 feet 

h 8 

Answers: 

79-40-00 

66-55-30 

27-59-00 
(lower limb) 

50-09-30 
(lower limb) 

W.T. of Transit 

12-01-01.1 

11-57-15.9 

8-17-07.1 p.m. 

6-22-05 p.m. 

Lat. at Transit 

33-06-23 S. 

38-15-35 N. 

48-57-34 N. 

34-37-14 S. 













OBSERVATIONS FOR LATITUDE. 


31 



Problem 5 

Problem 6 

Problem 7 

Problem 8 

Body 

Denebola 

Vega 

Jupiter 

Venus 

Date 

2 July, 1925 

4 May, 1925 

3 Oct., 1925 

4 Oct., 1925 

D.R. Lat. 

27-36-45 S. 

59-30-15 N. 

39-48 N. 

16-43 N. 

D.R. Long. 

82-15-12 E. 

22-01-00 W. 

74-38 W. 

127-18 E. 

C-W 

6-25-38 

1-12-32 

4-36-17 

3-55-58 

Chro. error 

fast 10“-37.2 8 

slow 12 111 —18.4 s 

slow 3 m -28 s 

fast 24 m -18.3 s 

I.C. 

(+) 2'-30" 

(-) 0'-45" 

(-) l'-00" 

T 

GO 

f 

© 

o 

Ht. of eye 

36 feet 

32 feet 

42 feet 

46 feet 

h s 

47-26-00 

69-21-00 

27-14-10 

53-56-00 

Answers: 





W.T. of Transit 

5-21-15.0 

3-51-20.2 

6-29-41.8 

2-23-54.5 p.r 

Lat. at Transit 

27-38-47 S. 

59-28-16 N. 

39-49-10 N. 

16-41-29 N. 

Given the data below find the 

latitude at time of sight. 



Problem 1 

Problem 2 

Problem 3 

Problem 4 

Body 

Sirius 

Denebola 

Venus 

Saturn 

Date 

2 Oct., 1925 

3 Jan., 1925 

2 Oct., 1925 

3 July, 1925 

D.R. Lat. 

45-15 N. 

10-00 s. 

26-17 N. 

35-03 N. 

D.R. Ix)ng. 

64-20-30 W. 

124-30-45 E. 

30-15-00 W. 

45-06 W. 

Watch 

5-50-00 a.m. 

5-32-00 a.m. 

2-20-00 p.m. 

7-35-00 p.m. 

C-W 

4-20-53 

3-05-10 

2-02-10 

3- 00-15 

Chro. error 

fast 03 m -55 8 

fast 03“- 32 s 

fast 01 m — 10 s 

slow 00 “-OS 8 

I.C. 

(-) 2'-00" 

(-) l'-00" 

(+) l'-OO" 

(+) 1-30" 

Ht. of eye 

46 feet 

48 feet 

36 feet 

40 feet 

h 8 

28-20-00 

65-00-00 

44-45-00 

43-15-00 

Answers: 





Latitude 

54-11-21 N. 

10-06-27 S. 

26-22-16 N. 

35-05-30 N. 


Problem 5 

Problem 6 



Body 

Moon 

Moon 




(lower limb) 

(upper limb) 



Date 

2 Jan., 1925 

2 July, 1925 



D.R. Lat. 

28-30 S. 

49-32 N. 



D.R. Long. 

47-00 W. 

167-00 E. 



Watch 

6-50-00 p.m. 

8-10-00 p.m. 



C-W 

2-58-21 

1-56-04 



Chro. error 

fast 00 m -40 s 

fast 56 m -19 s 



I.C. 

0'-00" 

(-)0'-30" 



Ht. of eye 

40 feet 

50 feet 



h s 

56-30-00 

28-01-00 




(lower limb) 

(upper limb) 



Answers: 





Latitude 

28-26-51.S. 

49-30-40 N. 




32 


OBSERVATIONS FOR LATITUDE. 


Given the data below find the noon constant; thence the constant for use with a 
reduction to the meridian taken at the indicated watch time. The h s given is taken 
at the indicated watch time. Find latitude at time of sight. 


Date 

D.R. Lat. 
D.R. Long. 
Watch 
C-W 

Chro. error 
I.C. 

Ht. of eye 
h 8 

Answers : 
Constant 

Latitude 


Date 

D.R. Lat. 
D.R. Long. 
Watch 
C-W 

Chro. error 
I.C. 

Ht. of eye 

h s 

Answers: 

Constant 

Latitude 


Problem 1 

1 May, 1925 
35-18-00 S. 
29-53-00 E. 
11-48-53 

10-00-59 
fast 2 m -18.4 s 
(—) 2'-15" 

24 feet 
39-29-30 


Kn = 74-53-32 
Kr =74-50-12 
35-20-42 S. 


Problem 5 

1 July, 1925 
12-25-00 N. 
59-20-04.5 W. 

11-55-21.6 
3-56-04 
fast O'MBO 8 
(+) l'-OO" 

42 feet 
78-51-25 


Problem 2 

4 Oct., 1925 
51-43-20 N. 
148-36-00 E. 
11-30-30.5 
1-59-06 
slow 6 m -27 8 
O'-OO" 

37 feet 
34-00-00 


Kn = 85-45-54 
Kr =85-37-21 
51-37-21 N. 


Problem 6 

1 Jan., 1925 
15-01-00 S. 
74-56-15 E. 
12-00-00.2 
6-59-23 
slow 0 m -21 s 
(+) 0'-45" 

28 feet 
81-48-00 


Problem 3 

3 Jan., 1925 
28-30-20 S. 
124-30-45 E. 

12-40-40.8 
3-05-10 
fast 03 m -32 a 
(-) l'-20" 

27 feet 
84-20-00 


Kn = 112-43-01 
Kr =112-38-37 
28-18-37 S. 


Problem 4 

3 May, 1925 
46-34-00 N. 
31-27-30 W. 
11-46-58.2 
2 - 11-11 
fast S 111 ^ 8 
(-) 00'-30" 
26 feet 
58-59-12 


Kn = 105-27-45 
Kr =105-23-35 
46-24-23 N. 


Kn (-) 66-42-20 Kn (-) 66-45-44 
Kr ( —) 66-26-20 Kr (-) 66-42-24 
12-25-05 N. 15-05-36 S. 


CHAPTER III. 

AZIMUTH. 


• a ^ mut ^ °I a body is the arc of the horizon intercepted between the north 

point oi the horizon and the vertical circle passing through the body. It is measured 
from the north point clockwise through 360°. It may also be defined as the angle at 
the zenith intercepted between the north branch of the observer’s meridian and the 
vertical circle through the body. Azimuth is simply another name for true bearing. 

r + e n n0 u th - P ° mt 2k a com P ass without error coincides in direction with the north point 
ol the horizon The compass is graduated to agree with the measurement of azimuth 
Irom 0 to 360 , clockwise. As the compass is so constructed that its card lays hori¬ 
zontal, i e., parallel to the plane of the horizon, a bearing of a body taken with a com¬ 
pass without error is the same as the body’s azimuth. The determination of the azi¬ 
muth ol a celestial body is an operation of frequent necessity. At sea the comparison 
ol a true bearing with a bearing as observed by compass affords the only method of 
determining the compass error. 

The meridian angle of a body is the smaller angle at the 
pole between the observer’s meridian and the circle of 
declination passing through the body, measured east or 
west, according as the body is east or west of the meridian, 
in time units, through 12 hours. If the body is west of the 
meridian it is the same angle as the body’s hour angle. If the 
body is east of the meridian it is equal to 24 hours minus the 
body’s hour angle. In the figure, a projection on the plane 
of the equinoctial, MPX is the meridian angle, and also 
the hour angle, of a body X. MPY is the meridian angle of a 
body, Y, = 24 h —H.A. The standard symbol for a meridian 
angle is “t.” 

When the observer’s latitude (L), the body’s meridian 
an gl e > L and the body’s declination (d) are known, the 
azimuth of a body may be computed. As the computation is too laborious for the 
navigator to perform every time he requires an azimuth, suitable tables, called 
azimuth tables, have been computed and are published by the Hydrographic Office. 
In these tables the values of the azimuth are tabulated for the various probable com¬ 
binations of L and d, in whole degrees, for 
every 10 minutes of the value of t. 


COMPUTATION OF THE AZIMUTH 
OF A BODY. 

32. Let the following be known: t, the 
meridian angle of the body, d, the body’s 
declination, L, the observer’s latitude. 
In the accompanying figure let PZA be 
the projection of the astronomical triangle 
on the plane of the horizon, with NS as 
the projection of the meridian, P the 
elevated pole, Z the zenith, and A the 
position of a body west of the meridian. 
The sides PA and PZ and the meridian 
angle t, are known. Gall the angle PZA, 
Z, call the angle PAZ, A. Two sides and 
the included angle of the astrononmical 
triangle being known it may be solved for Z, 
for from Napier’s analogies, 


N 



s 

Fig. 2. 



33 






34 


AZIMUTH. 


Tan (Z—A) =cot 3^ t sin y (L—d) sec y 2 (L + d) 

Tan y (Z+A) = cot y t cos x y (L—d) cosec y (L+d) 

Solving for 3^ (Z—A) and y (Z+A), and adding the results, we have Z. Let Z n = the 
body’s azimuth. Then, by inspection, 

Z n = 360°—Z. 


N 



Let the body be east of the meridian, in 
position A'. 

The solution is as before, except that the 
result of the solution is Z', which in this 
case, is the body’s true azimuth, Z n . 

If the observer is in south latitude, i. e., 
if the south pole is the elevated pole, the 
figure becomes as shown, (Fig. 3). The 
solution is as before, but if the body is west 
of the meridian (at A") then Z is measured 
from south to west, and Z n = 180°+Z. 

If the body is east of the meridian at 
(A'"), then Z is measured from south to 
east, and Z n = 180°—Z. 

The Azimuth Tables are computed and 
results tabulated for the above four cases, 
and cover all the probable combinations 
of latitude and declination with each ten 
minutes of the value of t. Hence in entering 
those tables use L, d, and t, as arguments. 


EXPLANATION OF THE RED AZIMUTH TABLES. 

33. Hydrographic Office Publication 71, known as the Red Azimuth Tables, was 
computed primarily for use with the sun, but must also be used for other bodies whose 
declinations are less than 23°. Separate pages are provided for each degree of the value 
of L from 0° to 70°. For convenience in working with the sun the tables are arranged 
with the argument t expressed as apparent time. In the right hand column of the page 
t appears under the caption “Apparent Time, P.M.”, and in the left column under 
“Apparent Time, A.M.” The left hand column is not available for use with other 
bodies than the sun. It is therefore better practice to disregard the left hand column; 
to always work with the right hand column, and to consider that column as under 
the heading “Meridian Angle, t.” 

In Figures 2 and 3, the value of the side AP is shown as 90—d. If the declination 
is south when the latitude is north, and vice versa, then the sign of d becomes (—). 
The value of the side AP then becomes 90—(—d) =90 + d. To provide for this the 
Red Azimuth Tables are divided into two parts, the pages of which are headed: 
“Declination Same Name as Latitude,” and “Declination Contrary Name to Latitude.” 

The values of Z are tabulated against t and d. These values of Z must be con¬ 
verted to Z n , according to the proof above. 

USE OF THE RED AZIMUTH TABLES. 

1 . Compute the meridian angle, t. 

2 . Enter the tables in the proper part, according as the latitude and declination 
are of the same or different names, and select the page headed with the value of the 
latitude. 

3. Select the declination column headed with the value of d. In this column 
select the value of Z tabulated against the value of t. 

4. In north latitude Z n = Z, if the body is east of the meridian, and 360°—Z if 
the body is west of the meridian. In south latitude Z n = 180°—Z if the body is east of 
the meridian, and 180°+Z if the body is west of the meridian. 






AZIMUTH. 


35 


4. (Alternative) Mark Z according to the rule at the bottom of the page, sub¬ 
stituting “when the body is east of the meridian” for “when the time is a. m.” and “the 
body is west of the meridian” for “when the time is p. m.” Then convert Z to Z n . 

4. (2nd Alternative) Remembering that in north latitude the tabulated values 
of Z are measured from the north point, and in south latitude from the south point, and 
to the east or west according as the body is east or west, draw a rough projection on the 
plane of the horizon and compute Z n . 


EXPLANATION OF THE BLUE AZIMUTH TABLES. 

(Hydrographic Office Publication No. 120.) 

34. These tables are computed and tabulated in the same manner as that de¬ 
scribed for the Red Tables, except that: 

1. The values of Z are tabulated for values of d 
from 24° to 70°, and hence are not used with the sun. 
Therefore the columns for t as an argument are not 
headed “Local Apparent Time” but simply “Hour 
Angle.” The latter, however, is incorrect, and should 
be considered to be “Meridian Angle, t.” 

2 . The tables are computed for latitudes and decli¬ 
nations of the same name only, but are available for 
use with latitudes and declinations of different names. 
To understand this consider the following: 

Two places, M and M', 180° apart on the same 
meridian, one in north latitude and the other in the 
same latitude, south, will have the same celestial 
horizon (see Figure 4). Let Figure 5 be a projection 
on the plane of that horizon, and P be the north pole. 
Then Z is the computed azimuth of a given body, 
X for the place in north latitude. The computed 
azimuth of the same body for the place in south 
latitude is measured from the south point of the horizon and is therefore SZX, the 
' supplement of Z. 



Fig. 4. 


Suppose you have a latitude and a decli¬ 
nation of different names to work with. 
Assume yourself shifted 180° in latitude on 
the same meridian. Your celestial horizon 
will be the same as before, your latitude will 
be numerically the same, but your latitude 
and declination will now be of the same name. 
However, the meridian angle of the body 
will now be measured from what was before 
the lower branch of the meridian, i. e., it will 
be the supplement of the meridian angle com¬ 
puted for your true position. With this 
supplementary meridian angle select the value 
of the computed azimuth. Gall this Z'. 
This will be the supplement of Z, the com¬ 
puted azimuth for your true position. There¬ 
fore, Z = 180—Z'. 


N 








36 


AZIMUTH. 


USE OF THE BLUE AZIMUTH TABLES. 

1. If the latitude and declination are of the same name. 

(a) Compute the meridian angle t, and mark it E or W. 

(b) Select the page for given latitude. 

(c) In the column for the given declination select the tabulated value of Z 

against the value of t. 

(d) Mark Z according to the rule at the bottom of the page and convert to Z n . 

2. If the latitude and declination are of different names. 

(a) Compute the meridian angle t, mark it E or W, and find its supplement t'. 
(d) Select the page for the given latitude. 

(c) In the column for the given declination select the tabulated value of Z' 

against the value of t'. 

(d) Find the supplement to Z' = Z. Mark it according to the rules at the 

bottom of the page, and convert to Z n . 


INTERPOLATING IN THE AZIMUTH TABLES. 

1 .. 35 ’ valaes of 1 Z may be selected from the Azimuth Tables without interpo¬ 

lation only when the values of L and d are in whole degrees and the value of “t” ends 
V o 1 i tei ! ”? inut f' ^or ® the 1 r cases resort must be had to interpolation. To inter- 
anH tL S rf e fi the va n e °* Z for th <? I * ext 1 ? wer whole degree of latitude and declination 
the base * 10 mmuteS ° f the tabu lated value of “t.” Call this value of Z 

v a I,,p T nf “t k ” eP Ti? d 38 u ef ° re ’ Sel f- t the vaIue of Z for the next hi e her tabulated 
value °i t. The difference between this and the base is the difference caused by a 

fere^e ^ t ?h C p h a Ilge l 0f r • F > nd . th e difference for 1 minute, and multiply by the dif¬ 
ference in the number of minutes in the given value oft, and “t” as used for the base. 

IN ext, using the values of t and L as used in the base, select the value of Z for the 

of /Pn l1l? n K deg - Cf, i re .ro r than u / ed in the base - T he difference between this value 
,l ( “ • il ls th , 6 dl ff e f ence . for one degree change of declination. Multiply by 

Sth of a degree 1 * 6 ^ ^ ° f * ™ ^ ^ USed in th ® baS6 ’ ex P re ssed to the nearest 

Repeat the operation for the latitude. 

Find the algebraic sum of all the corrections and apply to the base. 


Red Tables. Latitude and Declination, Same Name. 


t West. 


Example: At about 6:03 p.m., 2 January, 1925, in Lat 19 °- 30 'S Tnno- tp +l • . 


Base 

t 6-03 

d 22°.9 

L 19°.5 


w 

C-W 

6-03-21 

8-00-26 




C.T. 

Chro. fast 

14-03-47 * 

1-01.2 




G.C.T. 

Eq. T. 

14-02-45.8 (2 Jan.) 
(—) 4-05.8 

O’s dec. = 22°-56 / S. 



G.A.T. 

Long. E. 

13-58-40.0 

4-04-20.0 




L.A.T. 
t (W) 

t 

69-06 

68-22 
(-) 44 

4.4 

18-03-00 

6-03-00 

d 

69-06 

68-08 
(-) 58 

(-) 52.2 

L 

69-06 

69-13 
(+) 07 

(+) 3.5 

Cor. 

Z 

Z n 

69-06 

(-) 1-01 

S 68-05 W. 
248-05 

(-) 13.2 

(-) 13 

+ 4 


Z (psc) 

C.E. 

260-00 
11-55 W. 


Cor. (—) 1-01 


Var. 

Dev. 

10-00 W. 
1-55 W. 








re- 


AZIMUTH. 


37 


Red Tables. Latitude and Declination, Same Name, t East. 

Example: At about 7:30 a.m., 2 May, 1925, in Lat. 38°-08' N., Long. 147°-03' W., the navigator 
observes the sun to determine the deviation of the standard compass, as follows* W 7-28-37 C-W 
9-33-54, Chro. slow 3 m -07. I s , Z(p.s.c.) 76°-30', variation from chart 17° E. Find the deviation ’ 


Base 

t 4-39.5 

15.4° 
38.1 


w 

C-W 

7-28-37 

9-33-54 





C.T. 

Chro. slow 

17-02-31 

3-07.1 





G.C.T. 

Eq. T. 

G.A.T. 

Long. W. 

17-05-38.1 
(+) 3-03.9 
17-08-42.0 
9-48-12 

(2 May) 

O’s dec. = 15°-22.1' 

N. 


L.A.T. 

t 

7-20-30 
= 4-39-30 E. 




t 


d 

L 



91-31 

89-58 

91-31 

90-36 

91- 31 

92- 01 

Cor. 

91-31 
(-) 1-47 

(-) 1-33 

9.3 

(-) 

0-55 

.4 

(+) 30 

.1 

Z = 

z n 

N 89-44 E. 
89-44 

9.5 

(-) 

22.0 

(+) 3.0 

Z (psc) 

76-30 

465 

837 

(-) 

88 




(-) 88.35 

(+) 

110.0 

3 


C.E. 

13-14 E. 


Cor. (- 

-)107' = (- 

•)l°-47'. 

Var. 

Dev. 

17-00 E. 
3-46 W. 


Red Tables. Latitude and Declination, Different Names, t East. 

Example: At about 7:28 a.m., 3 October, 1925, Lat. 8°-33' N., Long. 162°-10' W., the sun is 
observed for deviation of standard compass as follows: W 7-28-03, C-W 10-37-40, Chro. slow 2“-00. s 6 
Z(p.s.c.) 81°, variation from chart 9°-30' E. 


W 

C-W 

c 

Chro. slow 

G.C.T. 

Eq. T. 

G.A.T. 
Long. W. 

L.A.T. 

t 


7-28-03 

10-37-40 

18-05-43 

2 - 00.6 

48-07-43.6 (3 Oct.) O’s dec. 3°-57.7'S. 
(+)10-56.3 


18-18-39.9 

10-48-40 

7-29-59.9 
= 4-30-00.1(E) 


Base 

t 4-30 
d 4° N. 

L 8°.6 S. 


t 

97-33 


d 

97-33 


97-33 
97-57 
+ 24 


.6 


Cor. (+) 14.4 


Cor. -f 
Z 

z n 

Z(p.s.c.) 

C.E. 

Yar. 

Dev. 


97-33 

14 

N 97-47 E. 


97-47 


81-00 
16-47 E. 
9-30 E. 
7-17 E. 





















38 


AZIMUTH. 


Red Tables. Latitude and Declination Different Name, t East. 

Example: 2 October, 1925, at about 4:00 a.m., in Lat. 10°-49' N., Long. 60°-ll'-45" E., observed 
the star a Canis Majoris, Sirius, for deviation of standard compass, as follows: W 3-58-02, C-W 7-59-30 
Chro. fast l m -59 8 , Z(p.s.c.) 133°-00', variation from chart 0. Find the deviation. 

W 3-58-02 

C-W 7-59-30 


C.T. 11-57-32 

Chro. fast 1-59 


G.C.T. 25-55-33 (1 Oct.) 

R.A.M.S. + 12 0-36-49.8 

Table III 3-55.8 Dec. = 16°-36.7' S. 


G.S.T. 00-36-18.6 

Long. E. 4-00-47 


L.S.T. 4-37-05.6 

☆’s R A. 6-41-51.6 


t (-) 2-04-46.0 E. 


t d 

Base 130-53 130-53 

t 2-04.8 128-36 132-05 

d 16.6 S. - - 

(-) 2-17 (+) 1-12 

L 10.8 N. 137 -72 

4.8 .6 

1096 +43.2 

548 

65.76 

(-) 66 


L 


130-53 


130-53 

131-47 

Cor. (+) 

20 

(+) 54 

Z 

N 131-13 E. 

.8 

Z n 

131-13 

+ 43.5 

+43.2 

Z(p.s.c.) 

133-00 

+86 

. -66 

C.E. 

l°-47' W. 

Cor. (+) 20 

Var. 

Dev. 

0-00 

r-47' w. 


Blue Tables. Two Cases, Latitude and Declination of the Same Name, and Latitude and 

Declination of Different Name. 


Example: 2 July, 1925, p.m., in Lat. 31-06 S., Long. 29-53-00 W., the navigator observes the star 
Star , B * the deviation of the compass as follows: 

W 6-28-13, C-W 2-04-00, Chro. slow l m -19 s , Z(p.s.c.) for Antares 114°; for Pollux 315°-30'. Variation 
from chart 20 W. 


w 

6-28-13 

C-W 

2-04-00 

C.T. 

8-32-13 

Chro. slow 

+ 1-19 

G.C.T. 

20-33-32 ( 

R.A.M.S. + 12 

18-38-03.4 

Table III 

3-22.7 

G.S.T. 

15-14-58.1 

Long. W. 

1-59-32.0 

L.S.T. 

13-15-26.1 

☆*s R.A. 

16-24-50.5 I 

t (-) 

3-09-24.4 E. 


(2 July) 


Dec. =26°-16' S. 





















AZIMUTH. 


39 



t 

d 

L 


Base 

t 3-09.6 

85-39 

84-34 

85-39 

84-08 

85- 39 

86- 51 

85-39 

Cor. ( —) 1-22 

d 26.3° S. (-) 

L 31.1 S. 

1-05 

65 

9.6 

I-) 1-31 (+) 1-12 

91 72 

.3 .1 

Z S 84-17 E. 

Z n 95-43 

Z (p.s.c.) 114-00 


390 

585 

(-) 27.3 

(-) 1-02 

+ 7.2 

C.E. 18-17 

Var. 20-00 W. 


62.40 

(+) 7.2 

• 

Dev. l°-43' E. 

(-) = 

l'-02" 

(-) 1-22 



Pollux: 



r 


L.S.T. 13-15-26.1 

☆*s R.A. 7-40-43 Dec. 28°- 

-12.5' N. 


t 5-34-43.1 W. 

Supplement 6-25-16.9 




t 

d 

L 


Base 

t 6-25.3 

63-20 

62-12 

63-20 

62-26 

63-20 

63-39 

63-20 

Cor. (—) 46 

d 28.2 N. ( 

L 31.1 S. 

-) 1-08 

6.8 

(—) 54 

.2 

(+) 9 

.1 

Z N 62-34 W. 

Z S 117-26 W. 


5.3 

(-) • 10.8 

.9 

Z n 297-26 


204 

340 

(-) 36 
+ 0.9 


Z (p.s.c.) 315-30 


(-) 36.04 

- 46 


C.E. 18-04 W. 

Var. 20-00 W. 





Dev. 1-56 E. 

Given the data below find the true azimuth. 




Problem 1 

Problem 2 

Problem 3 

Problem 4 

Body 

Date 

Latitude 

Longitude 

Watch 

C-W 

Chro. Error 

Sun 

3 Jan., 1925 
36-30-00 S. 
123-15-30 W. 
8-35-16 a.m. 
8-14-38 
slow 08 m -41 s 

Sun 

2 Jan., 1925 
24-18-30 N. 
62-45-15 E. 
4-27-52 p.m. 
7-16-48 
fast 06 m 28 s 

Vega 

3 Jan., 1925 
1-12-00 S. 
123-15-30 W. 
8-35-16 a.m. 
8-14-38 
slow 08 m 41 s 

Antares 

1 Mav, 1925 
30-42-00 S. 
47-35-30 W. 
4-31-59 a.m. 
3-38-16 
fast 01 m -09 s 

Answers: 

Zn 86-33 

Z n 233-36 

Z n 313-02 

Z n 263-57 


Problem 5 

Problem 6 

Problem 7 


Body 

Date 

Latitude 

Longitude 

Watch 

C-W 

Chro. Error 

Vega 

2 July, 1925 
0-23 'N. 
107-36-45 E. 
5-37-18 a.m. 
4-41-52 
slow 08 m -37 s 

Sun 

4 Oct., 1925 
7-45-15 S. 
153-18-00 E. 
7-53-12 a. m. 
1-42-36 
fast 2 m -13 8 

Sun 

3 Oct., 1925 
0-00 

107-36-45 E. 
8-01-15 a.m. 
4-41-52 
slow 08 m -37 8 


Answers: 

308-47 

90-10 

85-06 



Given t, d, and L, to find Z n for 23°-24° Declination. 

t d L 

3-33-58.1 E. 23-26.5 S. 35-26 N. 

Answer: Z n 131°-03' (East). 




















CHAPTER IV. 

LINES OF POSITION. 


36. A fix is an accurate determination of latitude and longitude. 

A line of position is the locus of the possible positions of a ship. Thus, if the true 
bearing oi a lighthouse from a ship is known, that bearing becomes a line of position. 
Again n the latitude has been obtained by the methods previously explained, a line 
may be drawn on the chart, running east and west in that latitude and extending 
through the probable longitudes. Such a line becomes a line of position. 

A line of position is not a fix, but if two lines of position are determined, their 
intersection is a fix. Thus, if a line of position obtained by a bearing of a known naviga¬ 
tional point, such as a light-house, can be crossed with a line obtained at the same time 
by a bearing of another navigational point, the intersection of the two lines is a fix. 

A line of position obtained at one time may be used at a subsequent time if it is 
moved parallel to itself a distance equal to the run of the ship in the interim and in the 
an ection of the run. Such a line of position is less accurate than a new line, because 
tne amount and direction of its movement must be determined by the usual dead reck¬ 
oning methods, and are subject to the errors of current, bad steering, and poor estimate 
oi speed. [Nevertheless, if two new lines cannot be obtained and crossed to obtain a 
hx, the fix obtained by a new line and an old line advanced is the most accurate that 
ca " wu 0f J F° 1 urs ^ * he accuracy of such a fix will be effected by the accuracy with 

w icn the run of the ship has been reckoned. In practice a navigator may use a very 
old line in this way, for, from his experience, he may be sure that his reckoning of the 
run is very close However, in the following pages it will be arbitrarily assumed 
that a line should not be advanced more than five hours. 

e ^ en . stated a line of position may be obtained in celo-navigation by means 

oi a sight lor latitude. However, it is more often obtained by means of a different 
type of observation. This latter method involves: 

(a) The ability to determine the altitude and azimuth of a given celestial bodv 

for a given point on the earth, at a given time. ’ 

(b) A knowledge of the principles of circles of equal altitudes. 

COMPUTATION OF ALTITUDES. 

37. For a given point on the earth let L= the latitude, and \= the longitude 

* °r a given instant of time let (d) be the declination of a body whose altitude is to be 

computed for that instant. Then, the civil or sidereal time of the instant and the 
longitude of the place being known the meridian angle (t) of the body may be com- 
puted. The zenith distance (z) of the body and thence its altitude (H c ) may be com¬ 
puted from the formulae: ' 

(1) hav z = hav t cos L cos d+hav (L ~ d) 

(2) H c = 90—z ' 

• i” The P ro j e ?ti° n on th ? P la , ne of the horizon of two astronomical triangles is shown 
in r igure 1, to illustrate the relation of the functions in formula (1) above. 

A and B represent bodies west and east of the meridian respectively. It will be 
seen that for A the function (t) is the hour angle, while for “B” the value of (t) is 24 
hours H.A.-the meridian angle. However, since the haversine of 24 h —H A has the 
same value as the haversine of the H.A. the latter may always be used in the formula 
whether the body is east or west of the meridian. Therefore, either the hour angle or 
the meridian angle may be used in the equation for the value of t. Since however the 
meridian angle will be required for the determination of the azimuth, it is best always 

ll "” " ail,b '” f0r ll " determination otbofh 


40 



LINES OF POSITION. 


41 


. In Figure 1 the declination of A is shown as of the same name as the latitude, and 
the declination of B is of the different name. The polar distance of A is therefore 90—d, 

and of B is 90+ d. The 


N 



last term of formula (1) is 
the haversine of the differ¬ 
ence between sides of the 
astronomical triangle 
formed by the polar dis¬ 
tance and the co-latitude. 
For A this becomes (90—d) 
—(90—L) = L—d. For Bit 
becomes (90-j-d)—(90—L) 
= L+d. Hence in comput¬ 
ing the altitudes, use the 
haversine of the difference 
between the latitude and 
declination if they are of 
the same name, and of the 
sum if they are of different 
names. 

It should be noted that 
a computed altitude is a 
geocentric altitude, i. e., 
the altitude as it would be 
observed at the center of 
the earth with an horizon 
parallel to the observer’s 
horizon on the surface. 


CIRCLES OF EQUAL ALTITUDES. 



38. When a sextant altitude is corrected to make it available for use in the solu¬ 
tion of the astronomical triangle, one of the corrections applied is that for parallax. 
The effect of this correction is to make the corrected altitude a geocentric altitude. 
A geocentric altitude may be defined as the altitude which a body would have if it 
were at an infinite distance from the earth. This is shown in Figure 2. 

Let G represent any ce¬ 
lestial body, A, the position 
of an observer on the earth, 
the circle a vertical circle 
of the earth in the same 
plane as G. Then H'B' is 
the observer’s terrestial 
horizon, and HB is his 
celestial horizon. C'A is 
drawn parallel to CO. Then 
CAH' is the altitude of G 
as observed at A. AGO is 
the parallax of G = GAG'. 

This parallax is added to 
the altitude CAH', giving 
the corrected altitude 
C'AH'. This is the same 
altitude which would be 
observed if the body were 
at an infinite distance. 

In the following discus¬ 
sions and figures, the alti¬ 
tude used will be the fig. 2 . 













42 


LINES OF POSITION. 


altitude as corrected for parallax, that is, it will be considered that the direction from 
the body to the observer is the same as that from the body to the center of the earth. 

In Figure 3, let B be the position 
of another observer on the same 
vertical circle as A, and let OG be 
the direction from the center of 
the earth of any celestial body 
lying in the vertical circle BA. 
C"B and C'A are drawn parallel 
to GO. Then at this instant the 
corrected altitudes of C from A and 
B will be G'AX and C"BY, respec¬ 
tively. These altitudes, being the 
angles intercepted between parallel 
lines, by the horizons of A and B, 
differ by the amount of inclination 
of the horizons at A and B to each 
other =XMB = AOB. The angle 
AOB is measured by the arc AB, 
a part of a great circle of the earth. 
Therefore, since 1' of arc of a great 
circle of the earth is equal to 1 
mile, the corrected altitudes at A 
and B will differ in minutes by the number of miles between A and B. 

Figure 4 is constructed in the same 
manner as Figure 2. Suppose the figure 
to rotate about the line GO. Then A 
will describe a circle whose trace is AA'. 

The line HA will describe a cone, AHA'. 

G'A will describe a cylinder. Then 
everywhere on the circle AA' the altitude 
of G will be G'AH. Such a circle is called 
a circle of equal altitudes. 

Definition: For any body, a circle 
of equal altitude is a circle of the earth 
cut by a plane perpendicular to the line 
joining that body to the earth’s center. 

For a given instant there is a series 
of circles of equal altitudes for any 
body. 

Five such circles are shown in Fig¬ 
ure 5. 

All of these circles have their center 
on the line SO. They are therefore 
parallel circles. The radius of the circle 
EE', on which circle the altitude will be 
zero, will be OE, the radius of the earth. 

The radius of the circle AA', on which circle the altitude is 86°, is roughly 280 miles. 
The radii of all intermediate circles will be between 4000 miles and 280 miles. There¬ 
fore, if a small arc of a circle of equal altitudes, say 30 or 40 miles in length for altitudes 
less than 86 , is drawn upon a chart, it will be of such large radius that it will not vary 
appreciably from a straight line. For altitudes greater than 86° the line must be shorter, 
and for an altitude of 89° should not exceed 10 miles. 

In Figure 4, the circle of equal altitudes was shown to be generated by the rota¬ 
tion of the line C A, of which line the terrestial end, A, traced the circle. The direction 
of CA from A is the true bearing of the body G because GA lies in the plane through 
the observer s zenith, the center of the earth and the body. Therefore, at every point 
of the circle of equal altitudes the latter will be perpendicular to the true bearing of 








LINES OF POSITION. 


43 


the body from that point. Hence the straight line which represents an arc of the circle 
of equal altitudes of a body on a chart must be at right angles to the true bearing of 
that body. 



39. It has been shown that at any instant, for any body, there is a series of 
parallel circles of equal altitude upon the earth. If the altitude of such a body is 
observed, then the ship from which the observation is taken must be somewhere on 
that circle of equal altitude on which the altitude is the same as the observed altitude. 
As has been shown a straight line of moderate length may be drawn upon the chart 
to represent the circle of equal altitudes. Such a line, being the locus of the possible 
positions of the ship is a line of position. Its position upon the chart may be fixed as 
follows: 

For the D.R. position and time of the observation, the azimuth, or true bearing 
of the body may be determined, A line may then be drawn upon the chart through 
the D.R. position in the direction of the body’s bearing. Since a circle of equal alti¬ 
tudes is everywhere at right angles to the body’s bearing, any straight line drawn at 
right angles to the bearing line of the body will represent a circle of equal altitudes. 
This fixes the direction of the required line of position. With the direction determined, 
it is necessary only to fix one point in order to draw the line. To do this the altitude 
is computed for the D.R. position and the time of observation. The difference in 
minutes of arc, between the computed altitude and the observed altitude will be the 
difference in miles between the circles of equal altitude which pass through the D.R. 
position and the actual position of the ship. (See Fig. 3.) Further, the circle of equal 
altitudes representing the locus of possible actual positions of the ship will be toward 
the observed body from the D.R. position, if the observed altitude is greater then the 



44 


LINES OF POSITION. 


computed altitude. Similarly, the actual position will be away from the D.R. position 
if the observed altitude is less than the computed altitude. (See Fig. 5.) Therefore, 
the number of minutes in the altitude difference is measured as miles from the D.R. 
position on the bearing line, toward or away from the body. The line of position may 
then be drawn through the point thus determined, at right angles to the bearing line. 

The following two examples will illustrate the method and form for work for find¬ 
ing the calculated altitude and azimuth. The problems are plotted in Figure 6 to 
illustrate the method of determining a fix by simultaneous lines of position. Example 
1 is plotted in the upper part of the figure, and example 2 in the lower half. 


Fix the Sun Line and Bearing. 

Example 1. On 2 October, 1925, at about 7:35 A.M. in D.R. Position Lat.37°-17 / N., Long. 75°-27' 
W., the navigator of the U.S.S. Raleigh observed the sun for a line of position as follows: W 7-35-10; 
C-W 4-50-24; Chro. fast 3 m -03.9 8 , Ht. of eye 18 ft., I.C. (—) 1-00, h 8 ©15-39-07. At the same instant 
the assistant navigator obtained the true bearing of Hog Island Light, 285°. Required the fix. 



FIX BY SUN LINE AND BEARING. 
Sun. 


Lat. 37°-17' N. 

X 75°-27' W. 

= 5 h -01 m -48« 







t 

d 

L 


Base 

w 


7-35-10 


t 4-28.8 

108-06 

108-06 

108-06 


108-06 

C-W 


4-50-24 


d 3.5 S. 

106-24 

108-54 

108-24 

(- 

-) 1-01 

Chro. T. 


12-25-34 


L 37.3 N. (- 

) 102 

(+) 48 

(+) 18 

N 

107-05 

Chro. fast 

(-) 

3-03.9 


(- 

) 90 

(+) 24 

(+) 5 

Zn 

107-05 

G.C.T. 


12-22-30.1 

(2 Oct.) 

Eq.T. (+) 10-32.5 

Dec. 

(-) 3-28.6 

hs 


15-39-07 

Eq.T. 

(+) 

10-32.8 


Cor. (+) .3 

Cor. 

(+) 0.4 

I.C. 

(-) 

1-00 

G.A.T. 


12-33-02.9 


Eq.T. (+) 10-32.8 

d 

3-29.0 S. 

T. 46 

(+) 

8-35 

X (W.) 


5-01-48.0 





Sub. 

(+) 

0-03 

L.A.T. 


7-31-14.9 





Ho 


15-46-45 

t (E.) 


4-28-45.1 


1. hav. 9.48593 






L 


37-17 

N. 

1. cos. 9.90072 






d 


3-29 

S. 

l. cos. 9.99920 







1. hav. 9.38585 


n. hav. .24314 


L r+u d 

40-46 

n hav. 

.12131 

z 

74-16-15 

n. hav. 

.36445 

He 

15-43-45 



Ho 

15-46-45 



a 

3-00 

miles toward 















LINES OF POSITION. 


45 


Fix by Simultaneous Observation of Two Stars. 


Example 2 - 0? 2 July, 1925, during evening twilight, in D.R. position Lat. 36°-49' N., Long. 

75 -12 W., the navigator of the U.S.S. Detroit and his assistant took simultaneous observations of 
stars 0 Leonis (Denebola) and a Scorpii (Antares) for lines of positions as follows: W = 7-24-21; C-W 
5-03-39; Chro. slow 00 m -39.8 s , Ht. of eye 36 ft., I.C. (+) l'-30. h s Denebola 51°-20'-10"; h s Antares 
19 0 -27'-37". Required the lines of position and the fix. 


STAR FIX, SIMULTANEOUS OBSERVATIONS. 


2 July, 

1925. 


Denebola. 

Lat. 36-49 N. 



Ttl 










s^O 

Antares. 

X 

75-12 W. 







= 

5 h -00“ 

‘-48 s 


<sT X V 

X* 





t 

d 

L 

Base 





t 2-24.7- 

114-46 


114-46 

114-46 





d 15° N. 

112-17 Denebola 

115-56 (-) 

14 

V" 


* 

*A 

(-) 

149 

(+) 

70 N 

114-32 W. 

w 



7-24-21 

L 36.8 N. (-) 

70 

(+) 

56 Z„ 

245-28 






Antares 



C-W 



5-03-39 

Sup. t. 9-45.1 

33-13 

33-13 

33-13 

33-13 

Chro. T. 



0-28-00 

d 26.3 S. 

31-07 

32-42 

33-01 (-) 

1-23 





(-) 

126 (-) 

31 (-) 

12 

31-50 

Chro. slow 


(+) 

0-39.8 

L 36.8 N. (-) 

64 (-) 

9 (-) 

10 Z„ 

148-10 

G.C.T. 



0-28-39.8 (3 July) 






R.A.M.S. + 12 


18-41-59.9 

h s 51-20-10 



hs 

19-27-37 

T. Ill 



0-04.7 

I.C. (+) 1-30 



I.C. (+) 1-30 

G.S.T. 



19-10-44.4 

T. 46 (-) 6-40 



T. 46 (- 

) 8-37 

x (W.) 



5-00-48.0 

Ho 51 15-00 



Ho 

19-20-30 

L.S.T. 



14-09-56.4 


L.S.T. 

14-09-56.4 



R.A. 



11-45-14.4 

Denebola 

R.A. 

16-24-50.5 

Antares 

t (W.) 



2-24-42 

1. hav. 8.98404 

t (E.) 

2-14-54.1 

1. hav. 

8.92503 

L 



36-49-00 N. 

l. cos. 9.90339 

L 

36-49-00 N. 

1. cos. 

9.90339 

d 



14-59-30 N. 

1. cos. 9.98496 

d 

26-16-00. S. 

1. cos. 

9.95267 





1. hav. 8.87239 



1. hav. 

8.78109 





n. hav. .07454 



n. hav. 

.06041 

L^d 



21-49-30 

n. hav. .03584 

L^d 

63-05-00 

n. hav. 

.27365 

z 



38-48-30 

n. hav. .11038 

z 

70-37-00 

n. hav. 

.33406 

He 



51-11-30 

/ 

He 

19-23-00 



Ho 



51-15-00 


Ho 

19-20-30 



a 



3-30 miles toward 

a 

2-30 miles away 
































46 


LINES OF POSITION. 



Fig. 6. 






LINES OF POSITION. 


47 


DEFINITIONS RELATING TO LINES OF POSITION. 

PRINCIPLES FOR ADVANCING LINE OF POSITION. 

40. In Figure 7, AB is the line of position obtained by observation of a body 
whose line of bearing is CD. D is the dead reckoning position. In this case the 
observed altitude is less than the calculated altitude and the line is plotted away from 
the body. Then G, the intersection of the line of position and the line of bearing, is 
the computed point. When only one line of posi¬ 
tion is obtained, the computed point is the most 
probable position of the ship on that line. 

Current is the difference between the reckoned 
position for any instant and the position by fix for the 
same instant. The term is a very loose one, and em¬ 
braces everything that causes the D.R. position to 
be in error. It includes effects of ocean currents, bad 
steering, wind, the state of the sea, the foulness of 
the ship's bottom, and, in general, everything that 
causes the navigator’s account of the course and 
speed oyer the floor of the ocean to be in error. 

The set is the direction in which the current acts. 

The drift is the amount in miles per hour that the 
ship is carried in the direction of the set. 

At sea it is customary to divide the naviga¬ 
tional work into increments of one day’s duration 
extending from clock noon to clock noon. The noon 
position each day is used as the origin of the day’s 
work, or point of departure for that day. It is 
obvious that in case of leaving port or pilot waters 
that day may be shortened; but it continues until 
noon. Also, when changing the zone description, 
the day may not equal 24 hours. 

Dead reckoning is carried along with the day’s 
work and it is likewise limited by consecutive noons. 

The dead reckoning position (D.R.) at anytime may 
be defined as the position obtained by applying 
the run to the last point of departure or origin of 
the day’s work. 

The current reckoning position (G.R.) originates with the latest fix. It is dead 
reckoning from the latest fix. Therefore, in the earlier stages of the day’s work it 
may coincide with the D.R. position. 

The navigator’s position (N.P.) is the most favorable position or “best” position 
short of a fix. It is really the D.R. or C.R. position corrected for such current as 
may have been established. With only one line of position available the computed 
point is the navigator’s position. 

Current may be determined by means of a G.R. position and a fix, the line joining 
those points indicating the set by its direction, and the total drift by its length. The 
drift may be obtained by dividing the length in miles by the number of hours that have 
intervened between the preceding fix and the D.R. position. 

Current when established must be allowed for when advancing a line of position. 
In solving problems it will be assumed that the current established between the two 
latest fixes is always to be used, and all previous current data will be neglected. In the 
practice of navigation at sea, due regard must be had for the reliability of the current 
established. The unavoidable small errors in observations may cause an abnormal 
current to be indicated between fixes obtained at short intervals. Abnormal atmos¬ 
pheric conditions may have the same effect. As the student is not in possession of the 
facts sufficient to enable him to judge the situation, the rule will be to always use the 
latest current established unless notified not to do so. 

Total current cannot be obtained by means of a D.R. position and a single line 
of position, but some current information may be obtained therefrom. Thus, in Figure 



Fig. 7. 


48 


LINES OF POSITION. 


7, the line CD represents the effect of the component of the current that has acted at 
right angles to the line of position. If it is desired to advance the line of position with 
no complete current determination available, it can be assumed that the effect of cur¬ 
rent in the direction at right angles to the line of position will continue at the same rate. 
Thus assume the D.R. position, D, to have been obtained by plotting the run from a 
point of departure five hours before, and let DC = 5 miles. Then the effect of the cur¬ 
rent acting in the line DC has been 1 mile per hour. Now assume the ship to proceed 
on the same course and speed for three hours and that it is desired to advance the line 
AB for this run. Advance the D.R. position for the run to D', plotting DD' for the 
direction and distance run. Advance the computed point for the run to G'. Draw 
C N parallel to CD, and equal to three miles. Then N is the navigator’s position, for 
it is the best position obtainable other than a fix. C/ is called the current reckoning 
position since it is used as the point to which the current component is applied, to 
obtain the navigator’s position. 



A current component should never 
be used when an established current is 
available. 

41. Three points of the line of 
position have now been defined: the 
computed point, the navigator’s posi¬ 
tion and th e current reckoning position. 
Figure 8 will illustrate their use. A is 
a point of departure, AB is the run 
to time of simultaneous observations, 
G the fix from those observations. 
Then GB is the current. B is ad¬ 
vanced to D by dead reckoning to 
time of next observation. G is simi¬ 
larly advanced to E, which is the 
current reckoning point. The current 
is applied to E by drawing EF parallel 

to GB, and making = F is 

the navigator’s position before sight is 
taken. A single sight is taken, giving 
the line XY. G, the computed point, 
is the navigator’s position after sight. 
Continuing the run, the next current 
reckoning point is obtained by apply¬ 
ing the D.R. run to G. The current 
reckoning point is always run up from 
the best previous position. 

Examples 3 and 4 illustrate the 
method of obtaining a fix from obser¬ 
vations taken at different times. 
Example 3 is plotted in the lower 
part of Figure 9, and example 4 in 
the upper part of the same figure. 


Fig. S. 






LINES OF POSITION. 


49 


Fix by Planet Line of Position Crossed With Meridian Altitude of Sun. 

Example 3. A ship has steamed on course 345° true, speed 6 knots, since noon 1 January, 1925, 
without observations. At morning twilight 2 January observed the planet Venus for a line of position 
as follows: W 6-56-50; C-W 5-02-00; Chro. slow l m -07.3 8 ; h 3 17-13-11; Ht. of eye 14 ft., I.C. (-) 
0-30". The D.R. position at time of sight was Lat. 36°-28' N.; Long. 74°-58'-30" W. The ship then 
proceeds on same course and speed for 5 hrs. and 4 min. (until L.A.N.) when obtained latitude, by 
meridian altitude, to be 37°-07' N. Required Noon D.R., C.R., N.P., and fix. 


2 January, 1925. 


PLANET LINE OF POSITION. 
9 Venus 





Lat. 

X 


36°-28' N. 
74 o -58'-30 // W. 
4 h -59 m -54» 


W 

C-W 

Chro. T. 
Chro. slow 

G.C.T. 
RAMO + 12 

T. Ill 

G.S.T. 

L (W.) 

L.S.T. 

R.A. 

t (E.) 

L 

d 


6-56-50 

5- 02-00 

11-58-50 
( + ) 1-07.3 

11-59-57.3 (2 Jan.) 

6- 44-27.0 

1-58.3 


18-46-22.6 

4-59-54 

13-46-28.6 

16-53-17.0 

3-06-48.4 
36-28-00 N. 
21-27-42 S. 


57-55-42 

72-47-45 
17-12-15 
17-05 55 


3-06.8 
21.5 S. 


36.5 N. (-) 
(-) 


R.A. 

Cor. 

R.A. 


!. hav. 
1. cos. 

1. cos. 

1. hav. 

n. hav. 
n. hav. 

n. hav. 


t 

135-46 

133-50 

116 
79 


d 

135- 46 

136- 24 


(+) 

(+) 


\ 6-50-38 
(+) 2-39 


16-53-17 


9.19618 

9.90537 

9.96880 

9.07035 

.11759 

.23452 

.35211 


38 

19 


L 

135- 46 

136- 00 


(+) 

(+) 


Dec. 

Cor. 


14 

7 


hs 
I.C. 
T. 46 

Ho 


Base 
135-46 
(-) 0-53 


N 

Zn 


(+) 


134-53 E 
134-53 

21-22.3 S. 
5.4 


21-27.7 S. 


17-13-11 
(-) 0-30 

(-) 6-46 


17-05-55 


6-20 miles away 



















50 


LINES OF POSITION. 


Fix by Moon Line of Position Advanced and Crossed With Sun Line of Position. 

Example 4. On 3 October, 1925, at about 5:30 A.M., the U.S.S. B.obolink, with tow, is in D.R. 
Lat. 37°-50' N., Long. 75°-05'W. The navigator observes the lower limb of the moon for a line of 
position, as follows: W 5-50-00; C-W 5-02-00; Chro. slow l m -07 s .3; Ht. of eye 45 ft.; I.C. 0-00; h s C 
14-48-00. The speed is 6 knots and the course is 190° true. The last fix was obtained at 6:00 P.M. 
2 October. At 10:30 A.M. the sun is observed for a line of position and the following data obtained: 
a = 4 miles, Z n = 150°. Required, the lines of position, the D.R., C.R., N.P., and fix at 10:30 A.M. 


3 October. 

rrv 



MOON LINE OF POSITION. 
Moon. 


Lat. 

X = 


37°-50' N. 
75°-05' W. 
5 h -00 m -20 s 


W 

C-W 

Chro. T. 

Chro. slow 

G.C.T. 

R.A.M.S. + 12 

T. Ill 

G.S.T. 

X (W.) 

L.S.T. 

R.A. 

MW.) 

(l 


z. 

H c 

H, 


5 50-00 
5-02-00 

10-52-00 
(+) 1-07.3 


10-53-07.3 (3 Oct.) 
0-44-42.9 

1-47.3 


11-39-37.5 

5- 00-20.0 

6- 39-17.5 
1-42-44.0 

4- 56-33.5 
37-50-00 N. 

5- 16-18 N. 


32-33-42 

74-15-35 

15-44-25 

15-50-08 

5-43 miles toward 


4-56.6 
5.3 N. 

37.8 N. (-) 
.(-) 


R.A. 
T. IV 

R.A. 


1. hav. 
1. cos. 

1. cos. 

1. hav. 

n. hav. 
n. hav. 

n. hav. 


t 

96-39 

95-05 

94 
62 


(-) 

(-) 


d 

96-39 

95-49 

50 
15 


1-40-49 
( + ) 1-55 

1-42-44 


9.56033 

9.89752 

9.99816 

9.45601 

.28576 

.07860 

.36436 


(+) 

(+) 


L 

96-39 

96-57 

18 
14 


Dec. 
T. IV 


H. P. 

h s 

I. C. 
T. 49 


Base 
96-39 
(-) 1-03 

N 95-36 W. 
Z„ 264-24 

5-05.6 N. 
( + ) 10.7 

5-16.3 N. 


583 

14°-48'-00" 
(-) O'-OO" 

( + ) l°-02'-56" 


Ht. of eye ( —) 
Ho 


0'-48" 


15°-50'-08" 














LINES OF POSITION. 5] 



Fig. 9. 









52 


LINES OF POSITION. 


SPECIAL USES OF LINES OF POSITION. 

42. When on soundings, with only a single line of position available, a rough 
check on the position may be had by plotting the line on the chart for the instant at 
which an accurate sounding is taken. The position of the ship should then be at about 
that point on the line where the depth of water as given on the chart agrees with the 
result of the sounding. 

By using a little foresight, it will frequently be possible to obtain a line of position 
by an observation of a body at the time its bearing is at right angles to the course. 
The resultant line of position will be parallel to the course. When the line is plotted 
it will be apparent at once which way the ship is being set from the course, and how 

much. Similarly a line may be ob¬ 
tained when the celestial body bears 
dead ahead or astern, giving a line 
which cuts the course at right angles. 
This gives an excellent check on the 
run. 

It should be borne in mind that a 
line of position obtained by a bear¬ 
ing of a navigational point may be 
moved in the same manner as that 
described for lines obtained by obser¬ 
vations of celestial bodies. 

Thus in Figure 10, suppose a ship 
on the course XY. A and B are 
navigational points usually in sight 
at the same time. Visibility is low 
so that B cannot be seen when the 
bearing AX is taken. A is then lost, 
and after running the distance XX', 
B is sighted, bearing in the direction 
BM. AX is moved up for the run to 
A'X', and the fix obtained at F. 

A radio bearing may be used as a 
line of position in any of the ways 
above described. 



Problems. 

1. The U.S.S. New York en route from Manila, P.I., to Valparaiso, Chile, is in D.R. position Lat. 


8 *’ L° n &- 88°-27'-00" W., on 2 July, 1925. The navigator observes the sun for a line of position 
follows: W = 11-10-22 A.M.; C-W = 5-56-23, Chro. fast 2“-34 s , I.C. (-) 2'-30", Ht. of eye 42 ft., 
^ 99 11-30. Find the altitude difference and azimuth. Answers: a = 2'-19" towards, 


32 
as 

h s © 33 

2. On 2 May, 1925, in D.R. position Lat. 36°-00' S., Long. 167°-00' E., the navigator observed 
the sun as follows: W = 3-15-00 P.M. C-W = 1-56-04, Chro. fast 5Q™-19 S 6 * , Ht. of eye 45 ft., I.C. (+) 
2'-00", h s Q 19-13-30. Find the altitude difference and azimuth. Answers: a =2-56" away, Z n = 
306 51'. 


3. On 4 January, 1925, in D.R. position Lat. 19°-18' N., Long. 72°-43'-30" E., the navigator of a 
ship en route to Bombay observed the sun as follows: W = 3-24-33 P.M., C-W = 7-08-09 Chro. slow. 
3 m -50 s , h s Q 25-02-15, Ht. of eye 25 ft., I.C. (+) 0'-30". Find the altitude difference and azimuth 
Answers: a = 5'-33" towards, Z n = 231°-52'. 

4. On 4 October, 1925, at about 7:30 A.M. in D.R. position Lat. 37°-22'-15" N., Long. 74°-16'-00" 
W., observed the sun for a line of position as follows: W = 7-30-00, C-W = 4-28-03, Chro. slow 32 m -16 8 * .3 
h s 028—15-00, Ht. of eye 42 ft., I.C. (+) 1'—00". Find the altitude difference and azimuth. Answers* 
a = 1-32" away, Z n = 121°-21'. 


5. At sea 4 October, 1925, in D.R. position Lat. 48°-12'-15" S., Long. 31°-02'-45" W., during 
morning twilight, the navigator observed Sirius for a line of position as follows* W = 5-10-00 C-W = 
2-03-30, Chro. slow 1 m -10 8 , I.C. (+) 2'-15", Ht. of eye 37 ft., h s = 57-22-10. Find the altitude difference 
and azimuth. Answers: a = 00-58" towards, Z n = 18°-35'. 

6. During evening twilight on 2 October, 1925, the navigator of the U.S.S. Chaumont in D.R. 

w Slt a°no L in ^ Alf 8 ^ N ;^ L o? g ;4 410 ~? 4, W *’ observed the star Antares for a line of position as follows: 

W ^X 02 - 1 ;, C -, W J*S“ 10 " 24, C J hr °'. sl °^ 15m ~ 188 ’ h s = 31-18-15. I.C. = (- ) 1-15", Ht. of eye 35 ft. 

rind the altitude difference and azimuth. Answers: a = l'-54" away, Z n = 217°-38'. 


LINES OF POSITION. 


53 


7. At sea 2 July, 1925, in D.R. position Lat. 39°-38' S., Long. 169°-17' E,, during evening twilight 
observed the star Antares for a line of position as follows: W =5-10-00 P.M., C-W =00-33-09 Chro] 
fast 8 m -43 s , h 8 = 28-35-00, I.C. ( —) l'-OO", Ht. of eye 42 ft. Find the altitude difference and azimuth 
Answers: a = 5-48" away, Z n = 101°-48'. 

8. A vessel en route from Constantinople, Turkey, to Odessa, Russia, is in D.R. position Lat. 
46°—21' N., Long. 30°—32' E., on 2 May, 1925, P.M. At w.t. 7-21-14 observed the star Denebola for a 
line of position as follows: C-W =8-01-16, Chro. fast 3 m -21 s , I.C. (-) 1-30", Ht. of eye 28 ft., h s = 
34-15-15. Find the altitude difference and azimuth. Answers: a = l'-09" towards, Z n = 75°-03\ 

9. During evening twilight on 1 October, 1925, the navigator of a vessel in D.R. position Lat. 
42°-53' S., Long. 31°-40'-15" E., observed the planet Venus for a line of position as follows- W = 7-00-00 
C-W = Q- 57 - 1 ^LChro. slow 5“-18 s ,h s = 26-04-00, I.C. = (+) 1-45", Ht. of eye 54 ft. Find the altitude 
difference and azimuth. Answers: a = 3-59" towards, Z n = 268°-06'. 

10. On 2 July, 1925, P.M. in D.R. position Lat. 15°-06' N., Long. 134°-19'-15" W., the navigator 
observed planet Saturn for a line of position as follows: W = 6-45-00, C-W =8-51-16, Chro. slow 
8 m -43 s , I.C. ( —) 2'-30", Ht. of eye 36 ft., b s 60-05-00. Find the altitude difference and azimuth. 
Answers: a =2-52" away, Z n = 152°-37'. 

11.. On 2 January, 1925, P.M. in D.R. Lat. 21°—05 7 S., Long. 45°—40' E., the navigator observes the 
lower limb of the moon for a line of position as follows: W = 7-05-06, C-W =9-10-10, Chro. slow 01 m -00 8 
Ht. of eye 45 ft., I.C. O'-OO", h s C 62-30-00. Find the altitude difference and azimuth. Answers: 
a = 00-00-43" away, Z n = 154°-11'. 

12. At sea in D.R. position Lat. 26°-17' N., Long. 46°-02' W., on 3 May, 1925, P.M., the navigator 
of a vessel observed the moon’s lower limb for a line of position as follows: Wt. =4-50-15 C-W =3-08-16 
Chro. fast 4 m -08 s , I.C. ( + ) 2'-00", Ht. of eye 40 ft., h s = 37-22-00. Find the altitude difference and 
azimuth. Answers: a = 1-56" toward, Z n = 99°-14'. 


CHAPTER V. 


A NAVIGATOR’S WORK AT SEA. 


PREPARATIONS FOR LEAVING AND ENTERING PORT. 

43. Before leaving port for a voyage, and when preparing to enter pilot waters, 
the navigator should examine all charts which are to be used to see that they are fully 
corrected to date. He should then study the charts, Sailing Directions, Light Lists 
and Tide Tables to make himself familiar with the waters to be traversed, the dangers 
to navigation therein, the characteristics of lights, markings of the channel, state of 
the tide at the hour set for sailing, probable set and drift of currents, areas in which 
icebergs may be encountered, and what radio compass stations are available for use. 
The course to be followed in pilot waters should be laid down on the harbor chart and 
bearings of prominent navigation marks should be determined for the points where 
the course is to be changed. These bearings should be laid down and noted on the 
chart. If the captain desires a pilot, or if the port regulations require that a pilot 
should be on board when leaving the harbor, the navigator should notify the local 
pilot’s association or captain of the port. 

The vicinity of the magnetic compass should be examined to see that no magnetic 
material has been stowed there. The navigator should see that the gyro compass is 
started at least four hours before sailing hour. If possible the error of the magnetic 
and gyro compass should be checked before getting underway. The chart board should 
be put in order and the necessary charts and gear laid out. 

The chronometers are checked, the sextants, peloruses and azimuth circles ad¬ 
justed. Ihe sounding machine is overhauled and inventory made to insure that 
sufficient tubes are on hand. The lead lines are inspected for markings, to see that 
they are of proper length and placed in the chains ready for use. All steering gear 
from the several steering stations to the steering engine is carefully inspected and 
tested out, and arrangements for immediate shifting to hand steering should be 
included. 

The Submarine Signal Receiving Apparatus should be placed in efficient working 
condition. 

GENERAL DISCUSSION RELATING TO NAVIGATION WORK AT SEA. 

44. The cosine-haversine formula by which the line of position is most often 
obtained is universally applicable for all combinations of meridian angle, latitude and 
declination, but is not generally used when the coordinates are within the limits of 
Tables 26 and 27, Bowditch. 

There are several methods of obtaining the calculated altitude of celestial bodies 
without the use of logarithms; notably the methods of AQUINO, and that of H.O. 
publications 201 and 203. These short method? of finding the calculated altitude are 
not covered by the course of the Naval Academy, where, because of lack of time, only 
fundamentals can be taught. They should be studied when there is an opoortunity 
and adopted if they suit the preference of the individual. Their use undoubtedly 
results in a saving of time and labor. Such methods are based upon a tabulation of the 
calculated altitude for given coordinates. Interpolation for other values of the co¬ 
ordinates is arranged for, but in order to reduce interpolations to a minimum it is usual 
to select the calculated altitude for an assumed position for which the coordinates 
agree with those used in the tabulations. This will give the same line of position as 
would be obtained by using the navigator’s position and interpolating. But, if an 
assumed position is used, the current component, which was explained in the preceding 
chapter, must he obtained by dropping a perpendicular from the navigator s position on 
the line of position. The perpendicular from the assumed position must never be used as 
a current component. 


54 



THE NAVIGATOR’S WORK AT SEA. 


55 


It should be noted that lines of position which intersect at right angles give the 
most accurate fixes, other things being equal. While it is not often possible to select 
bodies whose bearings vary by 90°, this point should be borne in mind and when a 
choice is available those bodies whose bearings are most nearly at right angles should 
be selected. If an observation is taken when the body observed is on the prime vertical, 
i. e., when it bears east or west, a line is obtained which runs north and south. Such a 
line is independent of any error in the reckoned latitude, and should be obtained if 
possible. Similarly, a line may be obtained which runs east and west and is independ¬ 
ent of an error in reckoned longitude. This is the case of the meridian altitude. 

Observed altitudes of less than 15° should be regarded as unreliable due to the 
uncertain effect of refraction. Altitudes of above 10° may be used if nothing better is 
available. 

In taking observations with the sextant a series of at least five altitudes should 
be taken as rapidly as good observations can be had. A comparison of the differences 
in altitude with the differences in time between the five will usually show three obser¬ 
vations in which the differences in altitude are proportional to the differences in time. 
Any one of these three may be used as correct. 

The index error of the sextant should be determined every time the sextant is used. 

A planet, being brighter than the stars, may be observed during the lightest part 
of twilight, when the horizon is clearly illuminated. Observed altitudes of planets may 
therefore be taken when the conditions are best for accurate measurement. After a 
little practice the altitude of Venus may be taken in broad daylight, when its R.A. 
differs by at least two hours from the sun’s R.A. If its R.A. differs by less than two 
hours from that of the sun it will be in the brightly illuminated area surrounding the 
sun and will not be visible. As an aid in finding it the altitude and azimuth are calcu¬ 
lated in advance for a given time. At that time the sextant is set for the calculated 
altitude and held in the direction of the bearing. The planet will be seen in the horizon 
mirror, a small disc having the dead white color of the moon when seen by daylight. 
A telescope should be used in the sextant and both telescope lenses and sextant mirrors 
must be perfectly clean. 

In the method taught in the preceding pages the altitude of a planet is corrected 
by the use of the star column of Table 46, Row ditch. This correction is not complete 
for a planet; because the stars are at such a great distance from the earth that they 
have no measurable parallax, and that correction therefore is not included in Table 46. 
The correction for parallax for planets is small, not over 9" and may be omitted; or, 
if it is desired to use it, it may be determined by means of the horizontal parallax 
tabulated in the Nautical Almanac and Table 17, Rowditch. If a further refinement 
is desired the altitude may be corrected for the semi-diameter which also will be found 
in the Nautical Almanac and may amount to as much as O'.5. 

The speed of the ship may be obtained by the patent log, or by means of the engine 
revolution counter. The latter is more accurate, especially if curves have been pre¬ 
pared showing the speed of the ship corresponding to the revolutions for various 
conditions of draft and the foulness of the ship’s bottom. The reading of the patent 
log and the engine revolution counter should be recorded every hour, at times of 
changes in course, and at the time of taking observations. 

Observations for the determination of the compass error should be taken when 
the body observed bears nearly east or west, as it is then changing its azimuth very 
slowly, and an error in the reckoned meridian angle has the least effect on the result. 

The standard magnetic and gyro compass should be compared every half hour 
and the readings recorded. A change in the difference of their readings will then give 
an early indication of trouble in one or the other which must be investigated at once. 

FINDING THE INTERVAL TO L.A.N., TODD’S METHOD. 

45. The mean sun moves to the westward at the rate of 15° or 900', of longitude 
in one hour. This is also the average rate of movement in longitude of the apparent 
sun. In considering the movement of the apparent sun for small periods of time its 
average rate may be used without material error. The meridian angle of the sun is 
determined for an instant in the forenoon, and this meridian angle is reduced to min- 

utes (x) of arc. Then, at that instant the interval to L.A.N. will be hours. If the 


56 


THE NAVIGATOR’S WORK AT SEA. 


meridian angle is determined on a ship underway the interval to L. A.N. will be affected 
by the run of the ship Thus, if the ship is steaming to the eastward the rate of 
approach of the sun will be increased by the speed of the ship. Again, if the ship is 
steaming to the westward the rate of approach of the sun will be decreased by the 
speed of the ship. The current will affect the rate of approach of the sun in the same 
manner. Let A A = the number of MINUTES OF LONGITUDE that a ship on a 
given course and speed covers in one hour. Let AG be the number of MINUTES OF 
LONGITUDE that the current sets the ship in one hour. Then the interval to L. A.N., 
in hours, will be: 

meridian angle for a given instant expressed in minutes of arc. 

900 ± A \± AG 

In using the above method the Q *s meridian angle should be determined at time 
of A.M. sight by subtracting the longitude of the best position from the G.A.T. of 
sight. Thus is a fix obtained, use the longitude of the fix, otherwise use the 
longitude of the navigator’s position after sight (computed point). Similarly, use a 
fully established current if possible, otherwise a current component. A A and A G 
may be obtained from the chart or from the traverse tables, remembering that what 
is required is the minutes of longitude per hour. 

Example: The fix at time of A.M. sight, taken when watch read 7-30-11, is Lat. 37°- 33'. 5 N., Long. 
72°-20'.9 W. =4 h -49 m -23 s .6. W = 7-30-11, C-W = 4-55-51, Chro. 1-01 fast. The current is set 110°, 
drift, 0.5 miles. Course is 85° true, speed 10 knots. Find the interval to L.A.N. 


w 

C-W 

= 7-30-11 
= 4-55-51 

Long. 

= 72-20-54. 

= 4-49-23.6 

CF 

CC 

—12-26-02 (Chronometer Face) 

= (-) i-oi 



GCT 

ET 

= 12-25-01 (2 May) 

= (+) 3-02.5 



GAT 

X 

=12-28-03.5 
= 4-49-23.6 W. 



LAT 

t 

t 

= 7-38-39.9 
= 4-21-20.1 

261.33 

1NT. 

15 x 261.33 

900 + 12.6+0.6 


15 

261.33 

913.2 log 2.96057 

log 

log 

colog 

1.17609 

2.41719 

7.03943 


4.2925 

log 

.63271 

Interval = 4 h -17 m —33 s 

W.T. of sight = 7 h -30 m -l I s 

W.T. LAN =11-47-44 




46. If the course or speed is materially changed between forenoon sight and 
L.A.N. and in particular if any maneuvering is done during this period it will be neces¬ 
sary to allow for these changes in obtaining the time of L.A.N. If the Interval to L.A.N. 
based on a certain course and speed has already been found, and the time of L.A.N. 
and corresponding longitude obtained on this basis, a close approximation to the actual 
time of transit may be found by simply applying a correction for difference of longitude 
gained or lost due to the course or speed changes involved. Thus, if new conditions 
place the ship 10 minutes of longitude further to westward of original assumption for 
L.A.N., transit will be approximately 40 seconds later. However, a more accurate 
method is to solve again for interval to noon when the ship resumes a set course and 
speed. This does not involve the taking of a new sight, it is necessary only to find the 
L.A.T. corresponding to the new instant and to the longitude at that instant. Thus, 
in the above example, let it be assumed that the ship maneuvers on various courses 
at 15 knots from 8 to 11 a.m., when course 85° true, speed 10 knots is resumed. Assume 
that the plotted position of the ship at 11:00 watch time has been found to be Lat. 









THE NAVIGATOR’S WORK AT SEA. 


57 


37°-35', Long. 71°-35'.2.W. The L.A.T. corresponding to these conditions and the 
interval to noon are obtained by the standard method as follows: 


w 

C-W 

=11-00-00 

= 4-55-51 


= 71-35-12 W. 

= 4-46-20.8 

CF 

CC 

=15-55-51 
= (-) 1-01 fast 



GCT 

ET 

= 15-54-50 2 May 

= (+) 3-03.6 



GAT 

X 

= 15-57-53.6 
= 4-46-20.8 W. 



LAT 

t 

t 

= 11-11-32.8 
= 0-48-27.2 
= 48.453 Minutes 

Interval 

15 x 48.453 

900 + 12.6+0.6 


15 

48.453 

913.2 log 2.96057 

log 

log 

colog 

1.17609 

1.68532 

7.03943 


.79586 


9.90084 

Int. 

W.T. 

= 0 h -47 m -45. I s 
= ll h -00 m -00s 



W.T. LAN = ll h -47 m -45.I 8 




This method may of course be used even if no morning sight has been obtained 
and any resulting error will be practically proportional to the error in reckoned longi¬ 
tude, an error of 1 minute of arc causing an error of approximately 4 seconds of time. 

THE DAY’S WORK. 

47. The following is an outlne of the work required of the navigator every day 
at sea: 

Dead Reckoning. The dead reckoning is carried forward as pure dead reck¬ 
oning, regardless of fixes, from noon of one day to noon of the next day, or from time 
of departure to the succeeding noon. A comparison of the dead reckoning position at 
noon with the position by observation then gives the set and drift of the current for 
the preceding twenty-four hours. 

The compass error is determined daily. It should be determined at morning and 
afternoon observations of the sun, and if possible, whenever the course is changed. 

The sun should be observed in the forenoon and afternoon when on the prime 
vertical providing its altitude is then over 15°; otherwise as near the prime vertical as 
possible with an altitude exceeding 15°. The sun should also be observed at L.A.N. 

At morning and evening twilight a fix should be obtained by at least two stars, 
or a star and a planet, selected so that the lines of position intersect at approximately 
a right angle. 

Should any of the above observations be lost, due to clouds, or should circum¬ 
stances render it advisable, additional sights of the sun, the moon, or of Venus, should 
be taken during daylight. When no fix has been obtained at morning twilight it 
is often possible to obtain an excellent fix during daylight by simultaneous obser¬ 
vations of the sun and the moon or die sun and Venus. Lines of position obtained by 
observations as outlined above should be handled as described in the chapter on lines 
of position. 

At 8:00 a.m., at noon, and at 8:00 p.m. the navigator is required to make a written 
report to the captain giving the results of his work. This report includes the position 
by D.R., and by observation, the set and drift of the current, the deviation of the 
compass, the course and distance made good, and the course and distance to destination. 

The various steps of the navigator’s work have already been taken up in detail. 
In the following example the steps are assembled. Results given are those obtained 
by plotting, and differ slightly from results by compution. 








58 


THE NAVIGATOR’S WORK AT SEA. 



Obtaining Departure. 


Cross bearings. 

Time: 2:00 A.M. July 2, 1925 (Zone+5) 
“Highlands Light” bearing 255° true. 

“Nauset Light” bearing 212° true. 

/ Lat. 42-06-00 N. 

I Long. 69-44-40 W. 

Set course 85° true. 

Speed 9 knots. 

Weather overcast at dawn. No stars visible. 


2:00 A.M. Fix: 









THE NAVIGATOR’S WORK AT SEA. 


59 



Plate 2. 


8:00 A.M. D.R.: Lat. 42°-10'-20" N. Long. 68° T 32'-00" W. 

At 9:00 A.M. observed sun for line of position, obtaining following data: a =5 miles away, Zn —108 c 
true, Var. 16°-25' W., Z p.s.c. = 127°, Dev. 2°-35' W. 

Positions at 9:00 A.M.: 

D.R. Lat. 42°-ll'-00" N. 

C.P. Lat. 42°-12'-45" N. 


Current component: 
Current component in X = 


Long. 68°-19'-45" W. 
Long. 68°-26'-00" W. 

5 miles , 

—- = .71 knots 

7 hours 


6.5 

7 


= .93' per hr. (W) 


Speed component in X = 12.3' per hr. (E) 

Interval to L.A.N. =2.45 hrs. 

Run to L.A.N. = 9x2.45 = 22 miles. 

Current: . 71x2.45 = 1.7 miles. 

L.A.N. positions: 

D.R. Lat. 42-13-00 N. Long. 67-50-00 W. 

C.R. Lat. 42-14-45 N. Long. 67-56-30 W. 

N.P. Lat. 42-15-00 N. Long. 67-58-20 W. 

Meridian Latitude = 42-09-00 N. 

r a at v / Lat. 42-09-00 N. 

L.A.N. Fix: \ Long W. 

Run to clock noon = 5 miles (Current omitted). 

Clock noon D.R. Lat. 42-13-10 N. Long. 67-43-30 W. 

n1 u ri • f Lat. 42-09-10 N. 

Clock noon Fix: \ Long 67 _ 54 _ 3 o W . 

Established current: 

Set = 243°-30' 


_ 9.2 Mi. no . „ 

Drift = -rrr-u— = . 92 mi /hr. 

10 hrs. 

Made good: Course 87°-30' true, speed 8.1 knots. 

Note: The origin of the new D.R. is the clock noon fix. Continued course and speed until 2:00 
P.M. at which time ship crossed from Zone Description + 5 to Zone Description + 4. Set all ships 
clocks ahead ONE hour. 
















THE NAVIGATOR’S WORK AT SEA. 


60 



Plate 3. 


As before; on course 85° true, speed 9. 

At 4:35 P.M. observed sun on prime vertical for line of position, obtaining following data: 

Run to 4:35 P.M. = 3.6x9 = 32.4 miles. 

Current = 3.6x.92 = 3.3 miles. 

4:35 P.M. positions: 

D.R. and C.R. Lat. 42-12-00 N. Long. 67-10-50 W. 

N.P. Lat. 42-10-15 N. Long. 67-09-20 W. 

Fix: Lat. 42-10-15 N. Long. 67-12-20 W. 

Current: Set = 252°-50' 

Drift = |^| = 1.47 mi /hr. 


Continued course and speed until 8:00 P.M. when observation of stars gave following data: 

Run: 3.4 hrs. x 9 = 30.6 miles. 

Current = 1.47 x 3.4 = 5 miles. 

Polaris: Latitude 42-15-15 N. 

Denebola: a = 9.6 miles away Zn = 246° true. 

Antares: a = 3.6 miles towards Zn = 148° true. 

Current = none. 

8:00 P.M. Positions: 

D.R. Lat. 42-14-30 N Long. 66-28-40 W. 

C.R. Lat. 42-13-00 N. Long. 66-36-00 W. 

N.P. Lat. 42-12-30 N. Long. 66-42-25 W. 

Fix Lat. 42-14-30 N. Long. 66-28-40 W. 


Note : The center of the triangle formed by the stars’ lines of positions coincides 
Reckoning position, thus establishing the current as ZERO. 


with the Dead 












EXTRACTS FROM THE NAUTICAL ALMANAC, 1925. 

For use in connection with the problems 
contained in this book. 


01 






62 


EXTRACTS FROM THE NAUTICAL ALMANAC, 1925 . 


SUN, 1925. 


Day of 

Sidereal Time of 0 h Civil Time at Greenwich (R. A. M. S. + 12 1 *). 

Month. 

January. 

Ma>. 

July. 

October. 


h m s 

h m s 

h m s 

h m a 

1 

6 40 30.4 

14 33 36.9 

18 34 6.8 

0 36 49.8 

2 

6 44 27.0 

14 37 33.4 

18 38 3.4 

0 40 46.3 

3 

6 48 23.5 

14 41 30.0 

18 41 59.9 

0 44 42.9 

4 

6 52 20.1 

14 45 26.5 

18 45 56.5 

0 48 39.4 


JANUARY. 


MAY. 


JULY. 


G.C.T 

Sun’s 

Declination. 

Equation 
of Time. 

G.C.T 

Sun’s 

Declination. 

Equation 
of Time. 

G.C.T 

Sun’s 

Declination. 

Equation 
of Time. 

G.C . 1 


Thursday 1. 


Friday 1. 


Wednesday 1. 


h 


IQ S 

h 

o / 

m s 

h 

O / 

m s 

h 

0 

-23 3.S 

-3 20.9 

0 

+ 14 51.1 

+2 51.2 

0 

+23 10.C 

1 -3 27.6 

0 

2 

23 3.1 

3 23.2 

2 

14 52.6 

» 2 51.8 

2 

23 9.7 

3 28.6 

2 

4 

23 3.1 

3 25.6 

4 

14 54.2 

! 2 52.5 

4 

23 9.4 

3 29.6 

4 

6 

23 2.7 

3 28.0 

6 

14 55.7 

2 53.1 

6 

23 9.1 

3 30.6 

6 

8 

23 2.3 

3 30.4 

8 

14 57.2 

! 2 53.8 

8 

23 8.7 

3 31.5 

8 

10 

23 1.9 

3 32.8 

10 

14 58.7 

2 54.4 

10 

23 8.4 

3 32.5 

10 

12 

23 1.5 

3 35.1 

12 

15 0.2 

2 55.1 

12 

23 8.1 

3 33.5 

12 

14 

23 1.1 

3 37.5 

14 

15 1.8 

2 55.7 

14 

23 7.8 

3 34.4 

14 

16 

23 0.7 

3 39.9 

16 

15 3.3 

2 56.3 

16 

23 7.4 

3 35.4 

16 

18 

23 0.3 

3 42.2 

18 

15 4.8 

2 57.0 

18 

23 7.1 

3 36.4 

18 

20 

22 59.8 

3 44.6 

20 

15 6.3 

2 57.6 

20 

23 6.8 

3 37.3 

20 

22 

22 59.4 

3 47.0 

22 

15 7.8 

2 58.2 

22 

23 6.4 

3 38.3 

22 

H.D 

0.2 

1.2 

H.D 

0.8 

0.3 

H.D. 

0.2 

0.5 

H.D 


Friday 2. 


Saturday 2. 


Thursday 2. 


0 

-22 59.0 

-3 49.3 

0 

+ 15 9.3 

+2 58.8 

0 

+23 6.1 

-3 39.2 

0 

2 

22 58.6 

3 51.7 

2 

15 10.8 

2 59.4 

2 

23 5.7 

3 40.2 

2 

4 

22 58.1 

3 54.0 

4 

15 12.3 

3 0.0 

4 

23 5.4 

3 41.1 

4 

6 

22 57.7 

3 56.4 

6 

15 13.8 

3 0.6 

6 

23 5.0 

3 42.1 

6 

8 

22 57.3 

3 58.7 

8 

15 15.3 

3 1.2 

8 

23 4.7 

3 43.0 

8 

10 

22 56.8 

4 1.1 

10 

15 16.8 

3 1.8 

10 

23 4.3 

3 44.0 

10 

12 

22 56.4 

4 3.4 

12 

15 18.3 

3 2.4 

12 

23 4.0 

3 44.9 

12 

14 

22 56.0 

' 4 5.8 

14 

15 19.8 

3 3.0 

14 

23 3.6 

3 45.9 

14 

16 

22 55.5 

4 8.1 

16 

15 21.3 

3 3.6 

16 

23 3.2 

3 46.8 

16 

18 

22 55.1 

4 10.4 

18 

15 22.8 

3 4.2 

18 

23 2.9 

3 47.8 

18 

20 

22 54.6 

4 12.8 

20 

15 24.3 

3 4.8 

20 

23 2.5 

3 48.7 

20 

22 

22 54.2 

4 15.1 

22 

15 25.8 

3 5.4 

22 

23 2.1 

3 49.6 

22 

H.D. 

0.2 

1.2 

H.D. 

0.7 

0.3 

H.D. 

0.2 

0.5 

H.D 


Saturday 3. 


Sunday 3. 


Friday 3. 


0 

-22 53.7 

-4 17.4 

0 

+ 15 27.3 

+3 5.9 

0 

+23 1.8 

-3 50.6 

0 

2 

22 53.2 

4 19.8 

2 

15 28.8 

3 6.5 

2 

23 1.4 

3 51.5 

2 

4 

22 52.8 

4 22.1 

4 

15 30.2 

3 7.1 

4 

23 1.0 

3 52.4 

4 

6 

22 52.3 

4 24.4 

6 

15 31.7 

3 7.6 

6 

23 0.6 

3 53.4 

6 

8 

22 51.8 

4 26.7 

8 

15 33.2 

3'8.2 

8 

23 0.2 

3 54.3 

8 

10 

22 51.3 

4 29.0 

10 

15 34.7 

3 8.7 

10 

22 59.8 

3 55.2 

10 

12 

22 50.9 

4 31.3 

12 

15 36.2 

3 9.3 

12 

22 59.4 

3 56.1 

12 

14 

22 50.4 

4 33.7 

14 

15 37.6 

3 9.8 

14 

22 59.1 

3 57.1 

14 

16 

22 49.9 

4 36.0 

16 

15 39.1 

3 10.4 

16 

22 58.7 

3 58.0 

16 

18 

22 49.4 

4 38.3 

18 

15 40.6 

3 10.9 

18 

22 58.3 

3 58.9 

18 

20 

22 48.9 

4 40.6 

20 

15 42.0 

3 11.4 

20 

22 57.9 

3 59.8 

20 

22 

22 48.4 

4 42.9 

22 

15 43.5 

3 12.0 

22 

22 57.4 

4 0.7 

22 

H.D. 

0.2 

1.2 

H.D. 

0.7 

0.3 

H.D. 

0.2 

0.5 

H.D. 


Sunday 4. 


Monday 4. 


Saturday 4. 


(f 

-22 47.9 

-4 45.2 

0 

+ 15 45.0 

+3 12.5 

0 

+22 57.0 

-4 1.6 

0 

2 

22 47.4 

4 47.4 

2 

15 46.4 

3 13.0 

2 

22 56.6 

4 2.5 

2 

4 

22 46.9 

4 49.7 

4 

15 47.9 

3 13.5 

4 

22 56.2 

4 3.4 

4 

6 

22 46.4 

4 52.0 

6 

15 49.4 

3 14.1 

6 

22 55.8 

4 4.3 

6 

8 

22 45.9 

4 54.3 

8 

15 50.8 

3 14.6 

8 

22 55.4 

4 5.2 

8 

10 

22 45.4 

4 56.6 

10 

15 52.3 

3 15.1 

10 

22 55.0 

4 6.1 

10 

12 

22 44.9 

4 58.9 

12 

15 53.7 

3 15.6 

12 

22 54.5 

4 7.0 

12 

14 

22 44.3 

5 1.1 

14 

15 55.2 

3 16.1 

14 

22 54.1 

4 7.9 

14 

16 

22 43.8 

5 3.4 

16 

15 56.6 

3 16.6 

16 

22 53.7 

4 8.8 

16 

18 

22 43.3 

5 5.7 

18 

15 58.1 

3 17.1 

18 

22 53.2 

4 9.7 

18 

20 

22 42.8 

5 8.0 

20 

15 59.5 

3 17.6 

20 

22 52.8 

4 10.6 

20 

22 

-22 42.2 

-5 10.2 

22 

+ 16 1.0 

+3 18.1 

22 

+22 52.4 

-4 11.5 

22 

H.D. 

0.3 

Note 

1.1 

!.— The Erma 

H.D. 

it inn nf 

0.7 

Timp ie tn K 

0.2 

P annlind Irv 1 

H.D. 

ikn P P 

0.2 

0.5 

H.D. 


OCTOBER. 


Sun’s 

Declination. 


Equation 
of Time. 


Thursday 1. 


-2 53.6 
2 55.6 
2 57.5 

2 59.5 

3 1.4 
3 3.4 
3 5.3 
3 7.2 
3 9.2 
3 11.1 
3 13.1 
3 15.0 

1.0 
Friday 2. 

3 16.9 +10 23.0 
10 24.6 
10 26.2 
10 27.8 


+ 10 3.6 
10 5.2 
10 6.8 
10 8.4 
10 10.1 
10 11.7 
10 13.3 
10 14.9 
10 16.5 
10 18.1 
10 19.7 
10 21.3 
0.8 


3 18.9 
3 20.8 
3 22.8 
3 24.7 
3 26.6 
3 28.6 
3 30.5 
3 32.4 
3 34.4 
3 36.3 
3 38.3 
1.0 


10 29.4 
10 31.0 
10 32.5 
10 34.1 
10 35.7 
10 37.3 
10 38.9 
10 40.5 
0.8 


Saturday 3. 

-.3 40.2 +10 42.1 


-4 

4 


3 42.1 
3 44.1 
3 46.0 
3 47.9 
3 49.9 
3 51.8 
3 53.7 
3 55.7 
3 57.6 

3 59.5 

4 1.5 
1.0 

Sunday 4. 
3.4 +11 


10 43.6 
10 45.2 
10 46.8 
10 48.3 
10 49.9 
10 51.5 
10 53.0 
10 54.6 
10 56.2 
10 57.7 
10 59.3 
0.8 


5.3 

7.3 
9.2 

11.1 
13.1 
15.0 

16.9 

18.9 
4 20.8 
4 22.7 

-4 24.7 

1.0 


11 
11 
11 
11 
11 
11 
11 
11 
11 
11 
+ 11 


0.8 

2.4 
3.9 

5.5 
7.0 

8.6 
10.1 
11.6 

13.2 

14.7 

16.2 

17.8 

0.8 


given. 




























































EXTRACTS FROM THE NAUTICAL ALMANAC, 1925 . 


63 


G.C.T. 


0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 


MOON, 1925. 


Right 

Ascension. 

Declination. 

S.D. 

HP. 


January 1. 


23 59 51 
0 3 59 
0 8 7 
0 12 14 

0 16 20 
0 20 25 
0 24 30 
0 28 33 


248 

248 

247 

246 

245 

245 

243 

243 


0 32 36 
0 36 39 243 
0 40 40 241 
0 44 41 


241 

241 


3 58.7 
3 36.4 
3 14.1 
2 51.8 


223 

223 

223 

223 


2 29.5 
2 7.2 

1 44 ' 9 223 
1 22.6 6 
222 


223 

223 


+ 


1 0.4 
0 38.2 
0 16.0 
0 6.1 


222 

222 

221 

220 


15.6 

15.6 

15.6 

15.6 

15.6 

15.5 

15.5 

15.5 

15.5 

15.5 

15.4 

15.4 


57.3 

57.2 

57.1 

57.1 

57.0 

56.9 

56.8 

56.8 

56.7 

56.6 

56.5 

56.5 


January 2. 


0 

2 

4 

6 

0 

0 

0 

1 

48 42 
52 42 
56 41 
0 40 

240 

239 

239 

239 

+ 0 
0 
1 
1 

28.1 

50.1 

12.0 

33.9 

220 

219 

219 

217 

15.4 

15.4 

15.4 

15.3 

56.4 

56.3 

56.3 

56.2 

0 

2 

4 

6 

9 

9 

9 

9 

33 

37 

41 

45 

10 

14 

18 

22 

244 

244 

244 

244 

+ 15 
15 
15 
14 

36.1 

21.7 

7.0 

51.9 

144 

147 

151 

153 

15.0 

15.0 

15.0 

15.0 

8 

10 

1 

1 

4 39 
8 37 

238 

OQ7 

1 

2 

55.6 

17.3 

217 

15.3 

15.3 

56.1 

56.1 

8 

10 

9 

9 

49 

53 

26 

29 

243 


14 

14 

36.6 

21.0 

156 

15.0 

15.0 

12 

1 

12 34 

ZO 4 

OQQ 

2 

38.9 

216 

15.3 

56.0 

12 

9 

57 

33 

244 


14 

5.0 

160 

15.0 

14 

1 

16 32 

zoo 

237 

3 

0.4 

215 

214 

15.3 

56.0 

14 

10 

1 

36 

243 

243 


13 

48.8 

162 

164 

15.1 

16 

1 

20 29 

236 

3 

21.8 

213 

15.3 

55.9 

16 

10 

5 

39 

243 


13 

32.4 

168 

15.1 

18 

1 

24 25 

3 

43.1 

15.2 

55.8 

18 

10 

9 

42 


13 

15.6 

15.1 

20 

1 

28 21 

236 

4 

4.3 

212 

15.2 

55.8 

20 

10 

13 

45 

243 


12 

58.6 

170 

15.1 

22 

1 

32 17 

236 

236 

4 

25.3 

210 

210 

15.2 

55.7 

22 

10 

17 

48 

243 

242 


12 

41.3 

173 

175 

15.1 




January 

3. 








May 

3. 




0 

2 

1 

1 

36 13 
40 9 

236 

+ 4 
5 

46.3 

7.1 

208 

15.2 

15.2 

55.7 

55.6 

0 

2 

10 

10 

21 

25 

50 

53 

243 

+ 12 
12 

23.8 

6.0 

178 

15.1 

15.1 

4 

1 

44 4 

235 

5 

27.8 

207 

15.2 

55.5 

4 

10 

29 

55 

242 


11 

47.9 

181 

15.2 

6 

1 

47 59 

235 

235 

5 

48.4 

206 

204 

15.1 

55.5 

6 

10 

33 

58 

243 

242 


11 

29.6 

183 

186 

15.2 

8 

10 

1 

1 

51 54 
55 49 

235 

OQS 

6 

6 

8.8 

29.1 

203 

om 

15.1 

15.1 

55.4 

55.4 

8 

10 

10 

10 

38 

42 

0 

3 

243 


11 

10 

11.0 

52.2 

188 

15.2 

15.2 

12 

1 

59 44 

Zoo 

OQA 

6 

49.2 

ZUJL 

onn 

15.1 

55.3 

12 

10 

46 

5 

242 


10 

33.2 

190 

15.2 

14 

2 

3 38 

zo4 

235 

7 

9.2 

zUU 

198 

15.1 

55.3 

14 

10 

50 

8 

243 

242 


10 

13.9 

193 

195 

15.2 

16 

2 

7 33 

234 

7 

29.0 

196 

15.1 

55.2 

16 

10 

54 

10 

243 


9 

54.4 

198 

15.2 

18 

2 

11 27 

7 

48.6 

15.1 

55.2 

18 

10 

58 

13 


9 

34.6 

15.3 

20 

2 

15 22 

235 

8 

8.1 

195 

15.1 

55.1 

20 

11 

2 

16 

243 


9 

14.7 

199 

15.3 

22 

2 

19 16 

234 

235 

8 

27.5 

194 

191 

15.0 

55.1 

22 

11 

6 

18 

242 

243 


8 

54.5 

202 

204 

15.3 




January - 

4. 








May 

4. 




0 

2 

23 11 


+ 8 

46.6 


15.0 

55.0 

0 

11 

10 

21 

243 

+ 

8 

34.1 

206 

15.3 

2 

2 

27 6 

235 

9 

5.6 

190 

15.0 

55.0 

2 

11 

14 

24 

8 

13.5 

15.3 

4 

2 

31 0 

234 

9 

24.4 

188 

15.0 

55.0 

4 

11 

18 

27 

243 


7 

52.7 

208 

15.3 

6 

2 

34 55 

235 

235 

9 

43.0 

186 

184 

15.0 

54.9 

6 

11 

22 

31 

244 

243 


7 

31.7 

210 

212 

15.4 

8 

2 

38 50 

235 

10 

1.4 

182 

15.0 

54.9 

8 

11 

26 

34 

244 


7 

10.5 

213 

15.4 

10 

2 

42 45 

10 

19.6 

15.0 

54.8 

10 

11 

30 

38 


6 

49.2 

15.4 

12 

2 

46 40 

235 

10 

37.6 

180 

15.0 

54.8 

12 

11 

34 

42 

244 


6 

27.6 

216 

15.4 

14 

2 

50 36 

236 

235 

10 

55.4 

178 

176 

14.9 

54.8 

14 

11 

38 

46 

244 

245 


6 

5.9 

217 

219 

15.4 

16 

2 

54 31 

236 

11 

13.0 

174 

14.9 

54.7 

16 

11 

42 

51 

244 


5 

44.0 

221 

15.5 

18 

2 

58 27 

11 

30.4 

14.9 

54.7 

18 

11 

46 

55 


5 

21.9 

15.5 

20 

3 

2 23 

236 

11 

47.5 

171 

14.9 

54.7 

20 

11 

51 

0 

245 


4 

59.7 

222 

15.5 

22 

3 

6 19 

236 

12 

4.5 

170 

14.9 

54.6 

22 

11 

55 

6 

246 


4 

37.4 

223 

15.5 

24 

3 

10 15 

236 

+ 12 

21.2 

167 

14.9 

54.6 

24 

11 

59 

12 

246 

+ 

4 

14.8 

226 

15.5 


G.C.T. 


Right 

Ascension. 

Declination. 

S.D. 

HP. 


May 1. 


0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 


247 


8 44 1 
8 48 8 247 

8 52 15 24 J 
8 56 21 £ 


0 28 
4 34 


246 

246 


9 
9 

9 8 40 OAK 

9 12 45 246 

9 16 51 
9 20 56 
9 25 1 
9 29 5 


245 

245 

244 

245 


+ 18 5 -°10fi 

17 54 - 4 10 
17 43 - 4 2 
17 32 ' 2 6 


17 20.6 
17 8.6 
16 56.4 
16 43.8 


120 

122 

126 

129 


16 3 °- 9 133 

16 17.6 433 
16 4.1 135 
15 50.3 


138 

142 


May 2. 


14.9 

14.9 

14.9 

14.9 

14.9 

14.9 

14.9 

14.9 

14.9 

14.9 

15.0 

15.0 


54.5 

54.5 

54.5 

54.6 

54.6 

54.6 

54.7 
54.7 

54.7 

54.8 
54.8 
54.8 


54.9 

54.9 

54.9 

55.0 

55.0 

55.1 

55.1 

55.2 

55.2 

55.3 

55.3 

55.4 


55.4 

55.5 

55.5 

55.6 

55.6 

55.7 

55.7 

55.8 

55.9 
55.9 
56.0 
56.0 


56.1 

56.2 

56.2 

56.3 

56.3 

56.4 
5.65 
5.65 

56.6 

56.7 

56.7 

56.8 

56.9 




















































64 


EXTRACTS FROM THE NAUTICAL ALMANAC, 1925 . 


b 

0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 


0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 


0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 


MOON, 1925.— Continued. 


G.C.T. 

Right 

Declination. 

S.D. 

H.P. 


Ascension. 





JuJ> 1. 


13 51 31 OK 

13 55 45 

14 0 0 
14 4 15 


254 

255 
255 
257 


14 8 32 
14 12 50 
14 17 10 
14 21 30 


258 

260 

260 

262 


14 25 52 268 
14 30 15 

14 34 39 266 
14 39 * 267 


5 54.1 

6 17.1 

6 39.9 

7 2.7 

7 25.5 

7 48.1 

8 10.6 
8 33.0 

8 55.4 

9 17.5 
9 39.6 

10 1.5 


230 

228 

228 

228 

226 

225 

224 

224 

221 

221 

219 

217 


15.7 

15.8 
15.8 
15.8 

15.8 

15.9 
15.9 
15.9 

15.9 

15.9 

16.0 

16.0 


57.7 

57.8 

57.8 

57.9 

58.0 

58.1 

58.2 

58.2 

58.3 

58.4 

58.5 

58.6 


July 2. 


0 

14 

43 

32 

269 

ocn 

-10 

23.2 

216 

16.0 

58.6 

0 

0 26 

36 

266 

- 2 

1.4 

256 

16.2 

2 

14 

48 

1 

10 

44.8 

16.0 

58.7 

2 

0 31 

2 

1 

35.8 

16.1 

4 

14 

52 

30 

2o9 

11 

6.) 

213 

16.0 

58.8 

4 

0 35 

26 

264 

1 

10.3 

255 

16.1 

6 

14 

57 

2 

Z1Z 

272 

11 

27.3 

212 

210 

16.1 

58.9 

6 

0 39 

51 

265 

264 

0 

44.8 

255 

256 

16.1 

8 

15 

1 

34 

275 

07C 

11 

48.3 

208 

one 

16.1 

59.0 

8 

0 44 

15 

263 

- 0 

19.2 

254 

16.1 

10 

15 

6 

9 

12 

9.1 

16.1 

59.0 

10 

0 48 

38 

+ 0 

6.2 

16.1 

12 

15 

10 

44 

Z ( O 

0*7 

12 

29.7 

zUo 

OOO 

16.1 

59.1 

12 

0 53 

1 

263 

0 

31.7 

255 

16.1 

14 

15 

15: 

21 

111 

279 

12 

50.0 

20 6 

201 

16.2 

59.2 

14 

0 57 

23 

262 

262 

0 

57.0 

253 

253 

16.1 

16 

15 

20 

0 

280 

OOO 

13 

10.1 

198 

16.2 

59.3 

16 

1 1 

45 

262 

1 

22.3 

253 

16.0 

18 

15 

24 ■ 

40 

13 

29.9 

16.2 

59.3 

18 

1 6 

7 

1 

47.6 

16.0 

20 

15 

29 : 

22 

ZqZ 

OOO 

13 

49.4 

195 

16.2 

59.4 

20 

1 10 

29 

262 

2 

12.7 

251 

16.0 

22 

15 

34 

5 

Z&o 

285 

14 

8.7 

193 

189 

16.2 

59.5 

22 

1 14 

50 

261 

260 

2 

37.8 

251 

249 

16.0 


July 3. 


16 37 49 305 

16 42 54 til 
16 48 0 
16 53 7 


306 

307 
309 


July 4. 

-17 47.5 
18 1.4 
18 14.9 
18 28.0 


16 58 16 

17 3 27 
17 8 38 
17 13 51 


311 

311 

313 

314 


17 19 5 315 

17 24 20 
17 29 37 i 1 ; 

17 34 54 319 


139 

135 

131 

125 


18 4 °' 5 120 

18 52.5 

19 4 -° 0 
19 15.0 

105 


19 25.5 
19 35.4 
19 44.7 
19 53.5 


99 

93 

88 

82 


16.5 

16.5 

16.5 

16.5 

16.5 

16.6 
16.6 
16.6 

16.6 

16.6 

16.6 

16.6 


60.4 

60.4 

60.5 

60.6 

60.6 

60.7 

60.7 

60.8 

60.8 

60.9 

60.9 

61.0 


G.C.T. 


Right 

Ascension. 


Declination. 


S.D. 


HP. 


October 1. 


0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 


23 32 45 
23 37 18 
23 41 50 
23 46 21 


273 

272 

271 

271 


23 50 52 270 

23 55 22 2 ™ 
23 59 52 

0 421 ™ 
0 8 49 MR 

013 17 !?* 

017 44 z, 

0 22 10 


6 39.4 fl 
5 6 

251 

5 24 ' 5 251 

4 594 253 

4 34 ' 1 253 
4 8.8 “ 

254 

3 43 ' 4 255 

3 17.9 HI 

2 52 - 4 255 

2 26.9 frf 

255 


16.3 

16.3 

16.3 

16.2 

16.2 

16.2 

16.2 

16.2 

16.2 

16.2 

16.2 

16.2 


October 2. 


October 3. 


0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 


258 

257 


2 10 58 
2 15 16 

2 19 3 3 258 
2 2 3 5 1 257 


2 28 8 258 

2 32 26 ilZ 

2 36 43 258 

2 41 1 HI 
257 


Octbober 4. 
+ 


257 


2 45 18 

2 4 9 3 5 257 

2 53 52 fl 
2 58 10 


7 50 ' 8 22R 

8 13.6 If 
8 36.1 2 f 

8 58.5 ™ 

9 20 ' 6 219 
9 42 - 5 

18 4-1 2 ® 
10 25.4 “ 

10 46.5 

11 7.4 

11 27 - 9 203 

11 48.2 Hi 

■ 199 


209 

205 


15.8 

15.8 

15.8 

15.7 

15.7 

15.7 

15.7 

15.7 

15.6 

15.6 

15.6 

15.6 


15 

38 

50 

OQC 

-14 

27.6 

187 

183 

1 OO 

16.3 

59.6 

0 

1 

19 

10 

260 

260 

+ 

3 

2.7 

249 

247 

16.0 

15 

15 

43 

48 

36 

24 

-<oO 

288 

ono 

14 

15 

46.3 

4.6 

16.3 

16.3 

59.6 

59.7 

2 

4 

1 

1 

23 

27 

30 

50 

3 

3 

27.6 

52.3 

16.0 

16.0 

15 

53 

14 

290 

291 

15 

22.6 

180 

176 

16.3 

59.8 

6 

1 

32 

10 

260 

260 


4 

16.9 

246 

244 

15.9 

15 

58 

5 

009 

15 

40.2 

1 *79 

16.3 

59.9 

8 

1 

36 

30 

259 


4 

41.3 


15.9 

16 

2 

58 

29o 

OQ4 

15 

57.5 

17o 

1 eo 

16.4 

59.9 

10 

1 

40 

49 


5 

5.6 

243 

15.9 

16 

7 

52 

OOK 

16 

14.4 

1 nn 

16.4 

60.0 

12 

1 

45 

8 

259 


5 

29.8 

242 

15.9 

16 

12 

47 

295 

298 

16 

31.0 

loo 

161 

16.4 

60.1 

14 

1 

49 

27 

259 

258 


5 

53.7 

239 

238 

15.9 

16 

17 

45 

OQQ 

16 

47.1 


16.4 

60.1 

16 

1 

53 

45 

259 


6 

17.5 


15.9 

16 

22 

43 

Zvo 

901 

17 

2.8 

157 

16.4 

60.2 

18 

1 

58 

4 


6 

41.1 

236 

15.8 

16 

16 

27 

32 

44 

46 

oUl 

302 

909 

17 

17 

18.2 

33.0 

154 

148 

1 \ r 

16.4 

16.5 

60.3 

60.3 

20 

22 

2 

2 

2 

6 

22 

40 

258 

258 


7 

7 

4.5 

27.8 

234 

233 

15.8 

15.8 

16 

37 

49 

0 U 0 

-17 

47.5 

145 

16.5 

60.4 

24 

2 

10 

58 

258 

+ 

7 

50.8 

230 

15.8 


59.6 

59.6 

59.6 

59.5 

59.5 

59.5 

59.4 

59.4 

59.4 

59.3 

59.3 

59.2 


59.2 

59.1 

59.1 

59.1 

59.0 

59.0 

58.9 

58.9 

58.8 

58.7 

58.7 

58.6 


58.6 

58.5 

58.5 

58.4 

58.3 

58.3 

58.2 

58.2 

58.1 

58.0 

58.0 

57.9 

57.8 


57.8 

57.8 

57.7 

57.7 

57.6 

57.5 

57.5 

57.4 

57.3 

57.3 

57.2 

57.1 



















































EXTRACTS FROM THE NAUTICAL ALMANAC, 1925. 65 


MOON, 1925.— Continued. 

TIME OF TRANSIT, MERIDIAN OF GREENWICH. 


Date. 

Greenwich 
Civil Time. 

Date. 

Greenwich 
Civil Time. 

Date. 

Greenwich 
Civil Time. 

Date. 

Greenwich 
Civil Time. 

Jan. 1 

2 

3 

4 

5 

h m 

17 53 

18 38 “ 

19 23 49 

20 7 44 

20 52 45 

May 1 

2 

3 

4 

5 

h m 

18 46 

19 32 49 

20 18 49 

21 4 tt 

21 52 48 

July 1 

2 

3 

4 

5 

h m 

19 57 53 

20 50 98 

21 47 l 7 

22 47 60 

23 51 64 

Oct. 1 

3 

4 

5 

h m 

23 45 51 

0 36 " 

1 25 tl 

2 14 49 

50 


VENUS, 1925. 

GREENWICH CIVIL TIME. 


Date. 

Apparent 

Right 

Ascension. 

Apparent 

Declination. 

Transit, 

Meridian 

of 

Green¬ 

wich. 

Date. 

Apparent 

Right 

Ascension. 

Apparent 

Declination. 

Transit, 

Meridian 

of 

Green¬ 

wich. 

Oh 

Oh 

Oh 

Oh 


h m s 

O / 

h m 


b m s 

o / 

h m 

Jan. 1 

16 45 21 _ 17 

" 21 10 - 8 115 

10 5 

May 1 

2 38 53 «n 

+14 42.7 _ 

12 6 

2 

16 50 38 8 ' 

21 22.3 ? 9 

10 7 

2 

2 43 43 % 

15 7.1 8« 

12 7 

3 

16 55 56 8 8 

21 33.2 99 

10 8 

3 

2 48 33 “0 

15 31.2 84’ 

12 8 

4 

17 1 14 8 J 8 

21 43.5 198 

10 10 

4 

2 53 24 80* 

15 54.8 

12 8 

5 

17 6 33 ™ 

21 53.2 H 

10 11 

5 

2 58 17 

16 18.0 ™ 

12 9 

July 1 

7 56 35 

+22 10.1 m 

13 23 

Oct. 1 

14 59 8 

-18 19.5 

14 23 

2 

8 1 46 l n 

21 56.8 | 88 

13 24 

2 

15 3 49 III 

18 42.7 “2 

14 24 

3 

8 6 56 

21 42 - 8 w 

13 26 

3 

15 8 31 

19 5.3 826 

14 24 

4 

8 12 5 899 

21 28.2 49 

13 27 

4 

15 13 14 SS 

19 27.6 828 

14 25 

5 

8 17 12 807 

21 13 -° 158 

13 28 

5 

15 17 58 » 

19 49 - 3 213 

14 26 


JUPITER, 1925. 

GREENWICH CIVIL TIME. 


Date. 

Apparent 

Right 

Ascension. 

Apparent 

Declination. 

Transit, 

Meridian 

of 

Green¬ 

wich. 

Date. 

Apparent 

Right 

Ascension. 

Apparent 

Declination. 

Transit, 

Meridian 

of 

Green¬ 

wich. 

Oh 

Oh 

0 h 

Oh 


h m s 

o / 

h m 

0 

h m s 

o / 

h m 

Jan. 1 

18 13 43 

-23 15.5 . 

11 32 

May 1 

19 36 42 _ 

-21 38.3 , 

5 2 

2 

18 14 43 99 

23 15.3 i 

11 29 

2 

19 36 49 ; 

21 38.2 ] 

4 58 

3 

18 15 42 «n 

23 15.0 8 

11 26 

3 

19 36 56 l 

21 38.1 | 

4 55 

4 

18 16 42 99 

23 14.7 8 

11 23 

4 

19 37 i : 

21 38.0 ; 

4 51 

5 

18 17 42 99 

59 

23 14.4 8 

11 20 

5 

19 37 6 l 

5 

21 37.9 l 

4 47 

July 1 

19 21 38 __ 

-22 19.5 19 

0 47 

Oct. 1 

18 58 31 1Q 

-23 7.1 , 

18 19 

2 

19 21 6 8 ; 

22 20.7 “ 

0 43 

2 

18 58 49 8 

23 6.7 4 

18 15 

3 

19 20 34 tt 

22 21.8 “ 

0 38 

3 

18 59 7 J 8 

23 6.3 4 

18 12 

4 

19 20 2 8 * 

22 23.0 

0 34 

4 

18 59 27 9 9 

23 5.9 4 

18 8 

5 

19 19 29 88 

22 24.2 12 

0 30 

5 

18 59 47 

23 5.5 4 

5 

18 4 





























































66 EXTRACTS FROM THE NAUTICAL ALMANAC, 1925 . 


SATURN, 1925. 

GREENWICH CIVIL TIME. 


Date. 

Apparent 

Right 

Ascension. 

Apparent 

Declination. 

Transit, 

Meridian 

of 

Green¬ 

wich. 

Oh 

0>> 


h m s 

o t 

h m 

Jan. 1 

14 41 23 I o 

-13 16.3 

8 0 

2 

14 41 42 J® 

13 17.6 ™ 

7 56 

3 

14 42 1 

13 18.9 ™ 

7 52 

4 

14 42 20 

13 20.1 

7 49 

5 

14 42 38 

lo 

13 21.3 

7 45 

July 1 

14 24 43 . 

-11 44.9 n 

19 47 

2 

14 24 39 ’ 

11 44.8 ; 

19 43 

3 

14 24 35 i 

11 44.8 V 

19 39 

4 

14 24 32 “ 

11 44.7 J 

19 35 

5 

14 24 29 1 

O 

11 44.8 1 

19 31 


Date. 

Apparent 

Right 

Ascension. 

Apparent 

Declination. 

Transit, 

Meridian 

of 


Oh 

Oh 

Green- 
i wich. 

May 1 

2 

3 

4 

5 

h m s 

14 37 58 18 
14 37 40 

14 37 23 

14 37 5 

14 36 47 ™ 

O f 

-12 39.0 

12 37 - 6 

12 36.2 

12 34.9 ] 6 A 
12 33.5 J; 

14 

h m 

0 4 
/ 0 0 

1 23 56 
23 52 
23 47 
23 43 

Oct. 1 

2 

3 

14 42 34 

14 42 59 

14 43 23 

- 13 32.9 

13 34.9 f® 
13 37.0 

14 4 
14 0 
13 57 

4 

14 43 48 H 

13 39.0 ;; 

13 53 

5 

14 44 14 H 

2o 

13 411 21 

13 50 


APPARENT PLACES OF STARS, 1925. 

FOR THE UPPER TRANSIT AT GREENWICH. 


Right Ascension. 


No. 

Constellation 

Name. 


Jan. 1. 

Feb. 1. 

Mar. 1. 

Apr. 1. 

May 1. 

June 1. 

July 1. 

Aug. 1. 

X 

GO 

! 

Oct. 1. 

Nov. 1. 

c5 

X 

Q 

Dec. 32. 

17 

a 

Can. Maj. 

6 

41 

51.3 

51.3 

50.9 

50.4 

49.8 

49.6 

49.6 

50.1 

50.8 

51.6 

52.5 

53.3 

53.7 

18 

e 

Can. Maj. 

6 

55 

41.7 

41.8 

41.4 

40.7 

40.1 

39.7 

39.7 

40.1 

40.8 

41.6 

42.6 

43.4 

43.9 

19 

a 

Can. Min. 

7 

35 

23.2 

23.4 

23.2 

22.7 

22.3 

22.0 

22.0 

22.3 

22.9 

23.7 

24.6 

25.5 

26.1 

* 20 

0 

Gemin. 

7 

40 

44.3 

44.6 

44.4 

43.9 

43.3 

43.0 

43.0 

43.4 

44.0 

44.9 

45.9 

46.9 

47.7 

21 

€ 

Argus 

8 

20 

61.2 

61.4 

60.9 

59.8 

58.6 

57.5 

56.9 

56.7 

57.2 

58.3 

59.7 

61.1 

62.1 

22 

X 

Argus 

9 

5 

15.5 

16.0 

15.9 

15.4 

14.6 

13.9 

13.5 

13.4 

13.6 

14.3 

15.3 

16.5 

17.4 

23 

0 

Argus 

9 

12 

26.8 

27.4 

27.1 

25.8 

24.1 

22.3 

20.9 

20.2 

20.4 

21.6 

23.4 

25.4 

27.1 

24 

a 

Hydrae. 

9 

23 

54.6 

55.1 

55.2 

54.9 

54.5 

54.1 

53.8 

53.8 

54.1 

54.6 

55.4 

56.4 

57.3 

25 

a 

Leonis 

10 

4 

22.9 

23.5 

23.8 

23.6 

23.3 

22.8 

22.6 

22.5 

22.7 

23.1 

23.9 

24.8 

25.8 

26 

a 

Urs. Maj. 

10 

59 

6.5 

7.9 

8.6 

8.5 

7.8 

6.8 

5.9 

5.2 

5.1 

5.6 

6.7 

8.3 

10.2 

27 

0 

Leonis 

11 

45 

13.7 

14.5 

15.1 

15.2 

15.1 

14.8 

14.4 

14.1 

14.0 

14.2 

14.7 

15.5 

16.5 

28 

a 

Crucis 

12 

22 

25.1 

26.7 

27.7 

28.0 

27.8 

27.1 

26.0 

25.0 

24.2 

24.0 

24.7 

26.0 

27.8 

29 

7 

Crucis 

12 

26 

59.6 

61.0 

61.8 

62.2 

62.1 

61.5 

60.7 

59.9 

59.2 

59.1 

59.6 

60.8 

62.4 

30 

0 

Crucis 

12 

43 

19.5 

21.0 

22.0 

22.5 

22.4 

21.9 

21.1 

20.1 

19.3 

19.1 

19.6 

20.8 

22.4 

31 

€ 

Urs. Maj. 

12 

50 

42.7 

44.2 

45.2 

45.8 

45.7 

45.1 

44.3 

43.5 

42.8 

42.6 

43.0 

43.9 

45.4 

32 

r 

Urs. Maj. 

13 

20 

53.0 

54.5 

55.6 

56.3 

56.3 

55.8 

55.1 

54.3 

53.5 

53.2 

53.3 

54.1 

55.4 

33 

a 

Virginis 

13 

21 

13.5 

14.4 

15.1 

15.6 

15.8 

15.7 

15.4 

15.0 

14.7 

14.6 

14.8 

15.4 

16.3 

34 

e 

Centauri 

14 

2 

14.6 

15.7 

16.6 

17.3 

17.6 

17.6 

17.3 

16.8 

16.3 

16.0 

16.1 

16.7 

17.7 

35 

a 

Bootis 

14 

12 

13.0 

14.0 

14.8 

15.4 

15.7 

15.7 

15.5 

15.0 

14.6 

14.3 

14.3 

14.7 

15.6 

36 

a 

Centauri 

14 

34 

28.4 

30.1 

31.5 

32.6 

33.2 

33.2 

32.6 

31.7 

30.6 

29.8 

29.7 

30.4 

31.9 

37 

0 

Urs. Min. 

14 

50 

50.6 

53.1 

55.5 

57.5 

58.3 

57.8 

56.2 

54.0 

51.6 

49.8 

48.8 

49.1 

50.7 

38 

a 

Cor. Bor. 

15 

31 

28.9 

29.9 

30.8 

31.6 

32.1 

32.3 

32.2 

31.8 

31.3 

30.7 

30.5 

30.7 

31.3 

39 

8 

Scorpii 

15 

55 

51.9 

52.8 

53.7 

54.6 

55.2 

55.6 

55.7 

55.4 

54.9 

54.4 

54.2 

54.4 

55.1 

40 

a 

Scorpii 

16 

24 

46.3 

47.2 

48.2 

49.1 

49.9 

50.4 

50.5 

50.3 

49.8 

49.3 

48.9 

49.1 

49.7 

41 

a 

Tri. Aust. 

16 

40 

38.1 

40.1 

42.2 

44.4 

46.2 

47.3 

47.5 

46.7 

45.3 

43.8 

42.7 

42.7 

43.8 

42 

V 

Ophiuchi 

17 

6 

2.4 

3.2 

4.0 

5.0 

5.7 

6.3 

6.6 

6.4 

6.0 

5.5 

5.1 

5.1 

5.6 

43 

X 

Scorpii 

17 

28 

28.3 

29.2 

30.2 

31.3 

32.3 

33.0 

33.4 

33.3 

32.8 

32.2 

31.7 

31.6 

32.1 

44 

a 

Ophiuchi 

17 

31 

25.2 

25.8 

26.6 

27.5 

28.2 

28.8 

29.1 

29.0 

28.6 

28.0 

27.5 

27.4 

27.7 

45 

7 

Draconis 

17 

54 

49.4 

50.1 

51.0 

52.3 

53.4 

54.1 

54.3 

54.0 

53.1 

52.1 

51.1 

50.6 

50.7 

46 

e 

Sagittarii 

18 

19 

9.0 

9.7 

10^6 

11.7 

12.7 

13.6 

14.1 

14.2 

13.9 

13.2 

12.7 

12.5 

12.7 

47 

a 

Lyrae 

18 

34 

21.8 

22.3 

23.0 

24.0 

25.0 

25.8 

26.2 

26.1 

25.6 

24.9 

24.1 

23.7 

23.7 














































EXTRACTS FROM THE NAUTICAL ALMANAC, 1925 . 67 


APPARENT PLACES OF STARS, 1925 .—Continued. 

FOR THE UPPER TRANSIT AT GREENWICH. 


Declination. 


No . 


Jan . 1 . 

Feb . 1 . 

Mar . 1 . 

Apr . 1 . 

May 1 . 

June 1 . 

July 1 . 

Aug . 1 . 

Sept . 1. 

Oct . 1. 

Nov . 1. 

Dec . 1. 

c 4 

CO 

6 

Q 

Special Name . 

Mag . 

17 

-16 

36.9 

37.0 

37.1 

37.1 

37.0 

37.0 

36.9 

36.8 

36.7 

36.7 

36.7 

36.8 

36.9 

Sirius 

-1.6 

18 

-28 

52.3 

52.4 

52.4 

52.5 

52.5 

52.4 

52.3 

52.1 

52.0 

52.0 

52.0 

52.1 

52.3 

Adhara 

1.6 

19 

+ 5 

25.0 

24.9 

24.9 

24.9 

24.9 

25.0 

25.0 

25.0 

25.1 

25.1 

25.0 

25.0 

24.9 

Procyon 

0.5 

20 

+28 

12.4 

12.4 

12.4 

12.5 

12.5 

12.5 

12.5 

12.4 

12.4 

12.4 

12.3 

12.3 

12.3 

Pollux 

1.2 

21 

-59 

16.0 

16.2 

16.3 

16.5 

16.5 

16.4 

16.3 

16.1 

16.0 

15.9 

15.9 

16.0 

16.1 


1.7 

22 

-43 

7.7 

7.8 

8.0 

8.1 

8.1 

8.1 

8 .G 

7.9 

7.7 

7.7 

7.6 

7.7 

7.9 


2.2 

23 

-69 

24.3 

24.5 

24.7 

24.8 

24.9 

24.9 

24.8 

24.7 

24.5 

24.4 

24.3 

24.4 

24.5 

Miaplacidus 

1.8 

24 

- 8 

20.0 

20.1 

20.1 

20.2 

20.2 

20.1 

20.1 

20.0 

20.0 

20.0 

20.0 

20.1 

20.2 

Alphard 

2.2 

25 

+ 12 

20.0 

19.9 

19.9 

19.9 

20.0 

20.0 

20.0 

20.0 

20.0 

20.0 

19.9 

19.8 

19.7 

Regulus 

1.3 

26 

+62 

9.1 

9.2 

9.3 

9.4 

9.5 

9.6 

9.6 

9.5 

9.3 

9.2 

9.0 

8.9 

8.8 

Dubhe 

2.0 

27 

+ 14 

59.4 

59.4 

59.4 

59.4 

59.4 

59.5 

59.5 

59.5 

59.5 

59.4 

59.4 

59.2 

59.1 

Denebola 

2.2 

28 

-62 

40.6 

40.8 

40.9 

41.4 

41.3 

41.3 

41.4 

41.3 

41.2 

41.1 

41.0 

40.9 

41.0 

Acrux 

1.1 

29 

-56 

41.2 

41.4 

41.5 

41.7 

41.8 

41.9 

41.9 

41.9 

41.8 

41.7 

41.5 

41.5 

41.6 


1.6 

30 

-59 

16.4 

16.5 

16.6 

16.8 

16.9 

17.1 

17.1 

17.0 

17.0 

16.8 

16.7 

16.7 

16.7 


1.5 

31 

+56 

21.8 

21.8 

21.8 

21.9 

22.1 

22.2 

22.2 

22.2 

22.1 

22.0 

21.8 

21.6 

21.5 

Alioth 

1.7 

32 

+55 

18.8 

18.8 

18.8 

18.9 

19.1 

19.2 

19.2 

19.2 

19.2 

19.0 

18.8 

18.7 

18.5 

Mizar 

2.2 

33 

-10 

46.1 

46.2 

46.2 

46.3 

46.3 

46.3 

46.3 

46.3 

46.2 

46.2 

46.2 

46.3 

46.4 

Spica 

1.2 

34 

-35 

59.8 

59.9 

60.0 

60.1 

60.2 

60.3 

60.3 

60.3 

60.2 

60.2 

60.1 

60.1 

60.1 


2.3 

35 

+ 19 

34.3 

34.2 

34.2 

34.2 

34.3 

34.4 

34.4 

34.5 

34.4 

34.4 

34.3 

34.2 

34.0 

Arcturus 

0.2 

36 

-60 

31.2 

31.2 

31.3 

31.4 

31.6 

31.7 

31.8 

31.8 

31.8 

31.7 

31.6 

31.5 

31.4 

Rigil Kentaurus 

0.1 

37 

+74 

27.6 

27.5 

27.5 

27.6 

27.7 

27.9 

28.2 

28.2 

28.0 

27.9 

27.7 

27.5 

27.3 

Kochab 

2.2 

38 

+26 

58.0 

57.9 

57.8 

57.8 

57.9 

58.0 

58.1 

58.2 

58.2 

58.2 

58.0 

57.9 

57.8 

Alphecca 

2.3 

39 

-22 

24.4 

24.4 

24.5 

24.5 

24.6 

24.6 

24.6 

24.6 

24.6 

24.6 

24.5 

24.5 

24.6 

Dschubba 

2.5 

40 

-26 

15.8 

15.8 

15.9 

15.9 

16.0 

16.0 

16.0 

16.0 

16.0 

16.0 

16.0 

16.0 

16.0 

Antares 

1.2 

41 

-68 

53.3 

53.2 

53.2 

53.3 

53.4 

53.5 

53.6 

53.7 

53.8 

53.7 

53.6 

53.5 

53.4 


1.9 

42 

-15 

37.9 

37.9 

37.9 

38.0 

38.0 

37.9 

37.9 

37.9 

37.9 

37.9 

37.9 

37.9 

38.0 

Sabik 

2.6 

43 

-37 

2.9 

2.8 

2.8 

2.9 

2.9 

2.9 

3.0 

3.0 

3.1 

3.1 

3.0 

3.0 

2.9 

Shaula 

1.7 

44 

+ 12 

36.9 

36.8 

36.7 

36.7 

36.7 

36.8 

36.9 

37.0 

37.0 

37.0 

37.0 

36.9 

36.8 

Rasalhague 

2.1 

45 

+51 

29.9 

29.7 

29.6 

29.6 

29.7 

29.8 

30.0 

30.1 

30.2 

30.2 

30.1 

30.0 

29.8 

Etamin 

2.4 

46 

-34 

25.2 

25.2 

25.1 

25.1 

25.1 

25.1 

25.2 

25.2 

25.3 

25.3 

25.3 

25.2 

25.2 

Kaus Australis 

2.0 

47 

+38 

42.9 

42.7 

42.6 

42.6 

42.6 

42 . 842.9 

43.0 

43.1 

43.2 

43.1 

43.0 

42.9 

Vega 

0.1 


































68_EXTRACTS FROM THE NAUTICAL ALMANAC, 1925 . 

MERIDIAN TRANSIT OF STARS. 1925. 


GREENWICH CIVIL TIME OF TRANSIT AT GREENWICH. 


Constellation 

Name. 

Mag. 

CC 

Feb. 1. 

Mar. 1. 

Apr. 1. 

j May 1. 

June 1. 

I *inf 

• -! 

Aug. 1. 

Sept. 1. 

u 

O 

Nov. 1. 

(J 

® 

O 

a Can. Maj. 

-1.6 

i o 1 

\ 23 57 

21 56 

20 5 

18 4 

16 6 

14 4 

12 6 

10 4 

8 2 

6 4 

4 2 

2 4 

e Can. Maj. 

1.6 

0 15 

22 9 

20 19 

18 17 

16 19 

14 18 

12 20 

10 18 

8 16 

6 18 

4 16 

2 18 

a Can. Min. 

0.5 

0 55 

22 49 

20 59 

18 57 

16 59 

14 57 

12 59 

10 57 

8 55 

6 57 

4 56 

2 58 

/3 Gemin. 

1.2 

1 0 

22 54 

21 4 

19 2 

17 4 

15 2 

13 4 

11 3 

9 1 

7 3 

5 1 

3 3 

e Argus 

1.7 

1 40 

23 34 

21 44 

19 42 

17 44 

15 43 

13 45 

11 43 

9 41 

7 43 

5 41 

3 43 

X Argus 

2.2 

2 24 

0 22 

22 28 

20 27 

18 28 

16 27 

14 29 

12 27 

10 25 

8 27 

6 25 

4 27 

jS Argus 

1.8 

2 31 

0 30 

22 36 

20 34 

18 36 

16 34 

14 36 

12 34 

10 32 

8 34 

6 32 

4 34 

a Hydrae 

2.2 

2 43 

0 41 

22 47 

20 45 

18 47 

16 45 

14 47 

12 46 

10 44 

8 46 

6 44 

4 46 

a Leonis 

1.3 

3 23 

1 21 

23 27 

21 26 

19 28 

17 26 

15 28 

13 26 

11 24 

9 26 

7 24 

5 26 

a Urs. Maj. 

2.0 

4 18 

2 16 

0 26 

22 20 

20 22 

18 20 

16 22 

14 21 

12 19 

10 21 

8 19 

6 21 

|8 Leonis 

' 2.2 

5 4 

3 2 

1 12 

23 6 

21 8 

19 6 

17 8 

15 6 

13 5 

11 7 

9 5 

7 7 

a Crucis 

1.1 

5 41 

3 39 

1 49 

23 43 

21 45 

19 43 

17 45 

15 44 

13 42 

11 44 

9 42 

7 44 

7 Crucis 

1.6 

5 46 

3 44 

1 54 

23 48 

21 50 

19 48 

17 50 

15 48 

13 46 

11 48 

9 46 

7 48 

/3 Crucis 

1.5 

6 2 

4 0 

2 10 

0 8 

22 6 

20 4 

18 6 

16 4 

14 2 

12 5 

10 3 

8 5 

e Urs. Maj. 

1.7 

6 9 

4 7 

2 17 

0 15 

22 13 

20 12 

18 14 

16 12 

14 10 

12 12 

10 10 

8 12 

f Urs. Maj. 

2.2 

! 6 39 

4 37 

2 47 

0 45 

22 44 

20 42 

18 44 

16 42 

14 40 

12 42 

10 40 

8 42 

a Virginis 

1.2 

6 40 

4 38 

2 48 

0 46 

22 44 

20 42 

18 44 

16 42 

14 40 

12 42 

10 40 

8 42 

6 Centauri 

2.3 | 

7 21 

5 19 

3 29 

1 27 

23 25 

21 23 

19 25 

17 23 

15 21 

13 23 

11 21 

9 23 

a Bootis 

0.2 

7 31 

5 29 

3 39 

1 37 

23 35 

21 33 

19 35 

17 33 

15 31 

13 33 

11 31 

9 33 

a Centauri 

0.1 

7 53 

5 51 

4 1 

1 59 

\ 0 1 
\ 23 57 

21 55 

19 57 

17 55 

15 53 

13 55 

11 54 

9 56 

/3 Urs. Min. 

2.2 ! 

8 9 

6 7 

4 17 

2 15 

0 17 

22 12 

20 14 

18 12 

16 10 

14 12 

12 10 

10 12 

a Cor. Bor. 

2.3 | 

8 50 

6 48 

4 58 

2 56 

0 58 

22 52 

20 54 

18 52 

16 50 

14 52 

12 50 

10 52 

8 Scorpii 

2.5 1 

9 14 

7 12 

5 22 

3 20 

1 22 

23 16 

21 18 

19 16 

17 15 

15 17 

13 15 

11 17 

a Scorpii 

L2 

9 43 

7 41 

5 51 

3 49 

1 51 

23 45 

21 47 

19 45 

17 43 

15 45 

13 44 

11 46 

a Tri. Aust. 

1.9 

9 59 

7 57 

6 7 

4 5 

2 7 

0 5 

22 3 

20 1 

17 59 

16 1 

14 0 

12 2 

7? Ophiuchi 

2.6 

10 24 

8 22 

6 32 

4 30 

2 32 

0 30 

22 28 

20 26 

18 25 

16 27 

14 25 

12 27 

X Scorpii 

1.7 

10 46 

8 44 

6 54 

4 52 

2 54 

0 53 

22 51 

20 49 

18 47 

16 49 

14 47 

12 49 

a Ophiuchi 

2.1 ! 

10 49 

8 47 

6 57 

4 55 

2 57 

0 56 

22 54 

20 52 

18 50 

16 52 

14 50 

12 52 

7 Draconis 

2.4 

11 13 

9 11 

7 21 

5 19 

3 21 

1 19 

23 17 

21 15 

19 13 

17 15 

15 13 

13 15 

e Sagittarii 

2.0 

11 37 

9 35 

7 45 

5 43 

3 45 

1 43 

23 41 

21 39 

19 37 

17 40 

15 38 

13 40 

a Lyrae 

0.1 

11 52 

. 

9 50 

8 0 

5 58 

4 0 

1 58 

t 0 0 
) 23 56 

21 55 

19 53 

17 55 

15 53 

13 55 


MERIDIAN TRANSIT OF STARS, 1925. 

CORRECTIONS TO BE APPLIED TO THE CIVIL TIME OF TRANSIT ON THE FIRST 
mvnPTHpK ™ 10 FIND THE CIVIL TIME OF TRANSIT ON ANY OTHER 

UAx UT 1 HEi IVLUIN 1 H. 


Day of Month. 

Correction. 

Day of Month. 

Correction. 

Day of Month. 

Correction. 

1 

h m 

0 0 

11 

h m 

-0 39 

21 

li m 

-1 19 

2 

-0 4 

12 

0 43 

22 

1 23 

3 

0 8 

13 

0 47 

23 

1 27 

4 

0 12 

14 

0 51 

24 

1 30 

5 

0 16 

15 

0 55 

25 

1 34 

6 

-0 20 

16 

—0 59 

26 

-1 38 

7 

0 24 

17 

1 3 

27 

1 42 

8 

0 28 

18 

1 7 

28 

1 46 

9 

0 31 

19 

1 11 

29 

1 50 

10 

0 35 

20 

1 15 

30 

1 54 

11 

ATT C xL , 

-0 39 

21 

-1 19 

31 

-1 58 


11 will.—II LUC quantity umen irom tnis taoie is greater than the civil time of 
increase that time by 23 h 56 m and then apply the correction taken from this table. 






























































EXTRACTS FROM THE NAUTICAL ALMANAC. 

, 1925. 

69 



TABLE I. 




FOR FINDING THE LATITUDE BY AN OBSERVED ALTITUDE OF POLARIS, 1925. 

Reduce the observed altitude of Polaris to the true altitude. 

Reduce the recorded time of observation to the local sidereal time. 

With this sidereal time take out the correction from the table below, and add it to or subtract 
it from the true altitude, according to its sign. The result is the approximate latitude of the place. 

Example. —June 10, 1925, at about 22 h 30 m (10 h 30 m P.M.), local civil time, when the Green¬ 
wich civil time is June 11, 3 h 36 m 30 8 , in longitude 74° west of Greenwich, suppose the true altitude 
of Polaris to be 39° 46', required the latitude of the place. 

Greenwich civil time. 3 36 30 

Greenwich sidereal time of 0 h Greenwich civil time, June 11, page 2 . 17 15 16 

Reduction from page 2 for Greenwich civil time.-f 0 36 

Greenwich sidereal time 

Longitude, 74° = . 



20 52 22 

4 56 0 

Local sidereal time 




15 56 22 

O / 

True altitude .... 

Correction from table below 



39 46 
+ 0 54 

Latitude 





+ 40 40 

Local S. T. 

0 h 

l h 

2 h 

3 h 

4 h 

5 h 

m 

o / 

O / 

O / 

O / 

o / 

O / 

0 

10 

20 

- 1 00 12 
; ijlo 

8 

-1 4.9 

1 53 9 

1 5.5 2 

-1 5.3 

1 4.9 4 

1 4.4 J 

-1 11 11 

1 10.0 

0 58.7 

-0 52.6 

0 50 - 9 In 

0 49.0 J 9 

-0 40.6 

0 38.3 23 

0 35.9 

30 

40 

50 

60 

-1 3.0 

1 3 - 8 l 

1 4.4 ? 

-1 4.9 5 

-i 5.6 

1 5.6 9 

1 55 2 
-1 5.3 2 

-1 3.7 _ 

1 30 9 

1 2.1 

-1 1.1 10 

-0 57.4 

0 55.9 15 

0 54.3 
-0 52.6 17 

-0 47.1 

0 45.0 2 j 

o 42.9 

-0 40.6 23 

-0 33.5 

0 31.0 f. 

0 28.4 29 
-0 25.8 26 

Local S. T. 

6 h 

7 h 

8 h 

9 h 

10 h 

ll h 

m 

O / 

O / 

O f 

O / 

O / 

O / 

0 

10 

20 

-0 25.8 

0 23.1 27 

0 20.4 27 

-° 9.3 

0 3.5 ^ 

+° 7,9 2 « 
o 10.7 28 

0 13.5 28 

+° 24 5 26 

0 27.1 29 

0 29.6 H 

+0 39.3 

0 41.6 23 

0 43.7 2 J 

+0 51.5 17 

0 53.2 7 

0 54.9 7 

15 

30 

40 

50 

60 

-0 17.7 

0 14.9 28 

0 12.1 28 
-0 9.3 28 

-° 0.7 

+0 2.2 H 

0 S -°29 

+0 7.9 29 

+0 16.3 

0 19.1 28 

0 21.8 27 
+0 24.5 27 

+0 32.2 

0 34.6 24 

0 37.0 24 
+0 39.3 28 

+° 45.8 

0 47.8 29 

0 49.7 9 
+0 51.5 18 

+0 56.4 

0 57.8 j 4 

0 59.1 13 
+ 1 0.2 11 

Local S. T. 

12 h 

13 h 

14 h 

15 h 

16 h 

17 h 

m 

O t 

O f 

O / 

O / 

O / 

O / 

0 

10 

20 

+ 1 °- 2 n 

1 L3 w 

1 2.3 19 

+ 1 4.9 

1 5.3 2 

1 5.5 2 

+ 1 5.3 

1 4.9 4 

1 4.4 J 

+ 1 1.3 

1 0-2 19 

0 59.0 12 

lo 

+0 53.1 

0 51.4 " 

0 49.6 ; 8 

iy 

+° 4L4 22 

0 39.2 22 

0 36.8 24 

AT 

30 

40 

50 

60 

+ 1 3.1 

1 3 - 9 l 

1 4.5 ® 

+ 1 4.9 4 

+ i 5.6 

1 5.6 ? 

1 55 2 
+ 1 5.3 2 

+1 3.8 

1 31 9 

1 2.2 9 

+ 1 1.3 9 

+0 57.7 

0 56.2 

0 54.7 ) 5 „ 
+0 53.1 lb 

+° 47 - 7 20 
0 45.7 f 

0 43.6 “ 

+0 41.4 

+0 34.4 

0 32.0 24 

0 29.4 29 
+0 26.9 25 

Local S. T. 

18 h 

19 h 

20 h 

21 h 

22 h 

23 h 

m 

o t 

O / 

O t 

O / 

O / 

O / 

0 

10 

20 

+0 26.9 

0 24.3 29 

0 21.6 27 

+° 10.5 

0 7 - 6 28 

0 4.8 28 

-o 6.6 

0 9 ‘ 5 28 

0 12.3 28 

-° 23 * 4 26 

0 26.0 29 

0 28.6 29 

-o 38.5 

0 40 - 8 22 

0 43.0 22 

-0 51.0 

0 52.8 8 

0 54.5 j 7 

30 

40 

50 

60 

+0 18.8 

0 1(U 28 

0 13.3 28 

+0 10.5 28 

+° 1,9 28 

0 0.9 28 

0 3.8 29 

-0 6.6 28 

-° 15A 28 

0 17.9 28 

0 20.7 28 

-0 23.4 27 

-° 3L2 25 

o 33.7 

0 36.1 ^ 
-0 38.5 24 

-° 45.2 

0 47.2 29 

0 49.2 29 
-0 51.0 18 

-0 56.0 1R 

0 57.5 

0 58.8 13 
-1 0.0 12 































































































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